Everton chairman Bill Kenwright has confirmed any fan who has bought shirts with Arteta or Beckford on this summer will get a refund.
Spanish ace Mikel Arteta and striker Jermaine Beckford made deadline-day
moves to Arsenal and Leicester respectively.
The Toffees raised about £14million from the deals, but as a gesture of goodwill Kenwright has made the offer.
"I have been contacted by several supporters (a lot with children) who had bought the new shirts with Mikel and Jermaine's surnames on the back of them," Kenwright told the club's website.
"Both players left the club quite literally at the very last minute on transfer deadline day.
"These are unusual circumstances and I simply want to try and play fair by those supporters who have spent hard-earned money on these shirts."