Chaos:
I would also like to see a date by the name of each player for when they are added to the list and suggest the following for the wording:
"I hereby agree to resign any game against another player on this list (in which both players have an effective date on or before the start of the game) if during the course of the game I move any piece back to the square it had vacated on the previous move."

For me the date is irrelevant. Fine by me if the rule applies to any of the games I'm playing already. But I'm perfectly ok with your definition if people prefer to have the dates added.

Chaos:
based on your post and that of Pedro, I agree.
No date should be necessary and leave out the part in the parenthesis on the description.

Dark Prince:
Slight change in wording for description so intent is not implied. That is if the illegal move is unintentional, inadvertent or unknown to the player, the agreement stands.
"I hereby agree to resign any game against another player on this list if during the course of the game any piece of mine is moved back to the square it had vacated on the previous move."

Dark Prince: Personally I'd prefer reversing the move if there are no side effects like identification (in whatever way) of pieces. Both players should agree ofcourse.

Chaos:
I'd prefer the bug were fixed and this wouldn't be an issue.
I don't intend to have games against players that aren't skilled enough to know a move is illegal or that a particular position could lead to such a move.
A player can look at the previous move prior to beginning the move and look at the move list during the move to verify that all pieces are moving according to the rules.
Anyone who doesn't want to risk making the agreement certainly doesn't have to.
Nevertheless, I don't mind adding to the description:
It will be at the players discretion against whom the illegal move was made to either ask the opponent to resign or allow the opponent the opportunity to have the illegal move reversed.

Chaos:
The agreement is indicated by having the name on the list.
Once the name is on the list, it will be up to the player against whom the illegal move was made to decide how to proceed and agreement by the opponent won't be needed if it's clear that an illegal move was in fact made.

Dark Prince:
What would be the point of having such a list otherwise?