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The position is legal. (proof game to follow sometime later when I have time).
Removing any piece does not result in a situation where the black king is in check.
A complete proof will require a proof game for each piece removed, which is too tedious. But it seems quite plausible that any piece removed still results in a legal game.

The position is legal.
Removing any piece does not result in a situation where the black king is in check.
A complete proof will require a proof game for each piece removed, which is too tedious. But it seems quite plausible that any piece removed still results in a legal game.

Black king couldn't have come from b7, since the checking knight at d6 has nowhere to retract to.
Pawns on c6 and e6 couldn't have come from d7 via capture since white has no missing piece.
No other black pieces have available space to retract to.
Therefore b7-b5 was black's last move.

Black king couldn't have come from b7, since the checking knight at d6 has nowhere to retract to.
Pawns on c6 and e6 couldn't have come from d7 via capture since white has no missing piece.
No other black pieces have available space to retract to.
Lastly, b5 couldn't have come from b6 since it is a check to white king.
Therefore b7-b5 was black's last move.

Appendix Contender for high scores:

Score: 28 (by removing the h6 pawn, since it is a witness, not an accessories). Still valid, since the missing white h-pawn cannot promote and be captured on d-file by black since there is only one missing black piece.