As with most warranty conditions, they request for proof of
purchase before servicing (not when sending in the card), but will
often honor the warranty even if such proof is not presented. In
this case, since you have the original undated warranty card, you
can send in the card whenever you feel like. (I wouldn’t wait too
long though) The warranty is only 1 year so it would have expired
anyway so you have nothing to lose by trying.