I think this is illogical. Chess games normally end when your King is gone. You cannot make moves after that, all your pieces die with it. So there should be no Time Thief to restore your King. This is the reason you cannot resolve a check by pinning the checking piece.
And in Spartan Chess, where the Spartans can promote to King, you cannot 'restore your King' with such a promotion and happily continue playing the move after your last King was captured.
You cannot make moves after that
That's the key word. After. The Time Thief steals a bit of time, he steals the last move of the opponent's piece.
Well, my most important concern is to make the rules consistent, even if they break with some concepts that are otherwise considered as fundamental for most Chess variants.
But I am very confident that this will not delay your project to incorporate all pieces ever presented on chess.com in Fairy Max by more than a day or so 
I am not convinced. It seems he needs positive time to do this himself: the Time Thief moves to a new location, where he might have never been before. That this makes others travel back in time is no help when the Time Thief is already dead.
Compare it to the following case: A Time Thief faces an enemy Rook, and the Rook captures it. Can the Time Thief restore itsef now? If so, where would he end up? In its old location, or replacing the Rook. Or would you have two Time Thiefs? If the answer is "no, the Time Thief cannot undo its own capture", then it should also not be able to restore capture of his King, as that is also his own capture. That is what 'royalty' means: capture the royal is capture of all.
The Time Thief can never undo his own capture, but I must admit that have forgotten to be clear about this scenario. If a Time Thieve is captured, his influence is totally gone.
as far as i remember, Capablanca proposed a sensible extra piece. Perhaps you could look it up ?? it may be ok for online chess
I don't recall reading that but I know Capablanca suggested trading the home squares of some pieces (I believe bishops and knights) in order to remove the "book" from openings. His recommendation made sense for two reasons. First, he was a brilliant player but wasn't really into studying openings. Second, in his day top masters played the QGD almost exclusively. Today's top masters play many different openings, including some that were considered old school in Capa's day.
The Time Thief can never undo his own capture, but I must admit that have forgotten to be clear about this scenario. If a Time Thieve is captured, his influence is totally gone.
But that is exactly the basis of my objection. Because capture of a King should be considered capture of the entire army. This is a basic assumption in Chess, that also underlies the fact that even pinned pieces can deliver check. You cannot draw after your King gets captured by such pieces through counter-striking at the enemy King with the piece that pinned it, because the piece that pinned it disappeared with its King.
So after the King gets captured, the Time Thief should be considered captured as well, and its influence totally gone.
Bulge piece:
Basically a piece that can move like a king, but it can not capture NOR can be captured.
So basically it is inoffensive but also indestructible.
It can be useful as a king shield or like an obstacle, a bulge.
- Why don't you do anything?
- Because we are the bulge
The Time Thief can never undo his own capture, but I must admit that have forgotten to be clear about this scenario. If a Time Thieve is captured, his influence is totally gone.
But that is exactly the basis of my objection. Because capture of a King should be considered capture of the entire army. This is a basic assumption in Chess, that also underlies the fact that even pinned pieces can deliver check. You cannot draw after your King gets captured by such pieces through counter-striking at the enemy King with the piece that pinned it, because the piece that pinned it disappeared with its King.
So after the King gets captured, the Time Thief should be considered captured as well, and its influence totally gone.
Sorry, the FIDE rules don't mention that capturing a King would mean to capture the entire army. You could consider this an unwritten rule, or an implicit common rule underlying all chess variants so far. Until the first variant is invented that steps out of these limit. The rules that I am providing for the Time Thief are consistent.
I've provided a link to another Time Travel variant on the chess variant pages, where it is possible to temporarily play without your King on the board. I am not the first.
And capturing a Time Thief sure means that the time Thief is gone. For a restoring move he must Queen-like 'see' the old square of his victim. From the table next to the board he clearly can't.
Some hardcore FIDE chess players strongly feel to the same extent that Chess 960 is already illogical, because a basic assumption in Chess is that a Rook can never be on e1 before the game has started. Can he?
I don't understand your final conclusion of your forelast posting. (Or is it an extra rule?) A Lumberjack might not capture normally, but it can capture 'abnormally', by knocking pieces off board, or into occupied squares. So what happens if the King is captured this way? You play on without the opponent having a King? That would be hard to win...
I would think that a situation where you can Knock a King of board should count as that King being in check.
This should be checkmate, right? (White to move.) It would be checkmate even with the black King on c6.
If the King is knocked off the board, it should count as having been captured, not as checkmated. Checkmated is when you cannot avoid being captured on the next move. If it could be knocked of the board in the next move, when it passes its turn, then it would be in check. If it cannot avoid being knocked of the board no matter how it moves (including turn pass), then it would be checkmate.
Here the King cannot move to d8, because it would be in check there:
(It is already in check on c8 as well.)
Oh, sorry, that is wrong. For a moment I forgot the Lumberjack only knocks orthogonally.
Why would your last diagram be checkmate? The Lumberjack can capture e7 by moving to e6. But it cannot move to e7 to knock the King. It is not supposed to capture normally (i.e by replacement).
Rontgen attack by Time thieve:
If the original square of the Time Thieve's victim is blocked by the victim itself (that is the case if the victim piece has moved towards the Time Thieve), then this is no impediment for the Time Thieve to make the capture.
This raises problems and I felt that I need to change this:
Currently the Time Thief is not seeing the current square of the white Bishop. After Bxc7 it would be unclear: the Time Thief would be able to capture the Bishop on f4 according to what I've mentioned so far. But I really don't like this. I'll change the rule in such a way that the Time Thief allways must see the capture square. That also means that candidate victims can walk towards the time thief without consequences. This way it is more simple and elegant, I think.
Wouldn't it be more elegant to say that the Time Thief first undoes the previous move, and then must be able to make the capture of the moving piece?
How about Castling, btw? Must the TT take the King to undo it, or can it also be the Rook?
Castling is considered as a King's move. The question however, is whether TTxK also would undo the Rook's movement from the corner to the center.
The King is not in check if he is indirectly protected by the restoring abilities of the friendly Time Thieve.
I did some rethinking, and after finding crazy or contradictionary scenario's I have decided to put some restrictions on this.
First I would like to define conditional check as the state where a King is attacked by enemy pieces, but after each capture the friendly Time Thief could restore his King.
An example: