The Christmas-themed card was delivered to Swansea Building Society’s Cradock Street branch last week even though it was originally sent in 1903 - so only just over a century too late.
Staff say they hope to find relatives of a Miss Lydia Davies, who previously lived at the address and who the card was addressed to, to reunite them with it.
The Royal Mail said it is likely the postcard was “put back into” its system, rather than “being lost in the post for over a century”.
“Timeliness, however, is not necessarily a consideration.”