Everton chairman Bill Kenwright has offered to refund fans who bought new shirts bearing the names Arteta or Beckford this summer.
Popular Spaniard Mikel Arteta and striker Jermaine Beckford made deadline-day moves to Arsenal and Leicester respectively. The Toffees raised about £14million from the deals, although they were completed so late manager David Moyes did not have time to utilise the cash.
Kenwright has come under fire from a small group of fans in the last fortnight for a lack of progress on selling the club, which is in need of major investment, and his goodwill gesture on the shirts is unlikely to cut him much slack with those growing increasingly frustrated at the ongoing situation at Goodison Park.
"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 said. "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.''
Any supporter who purchased the 2011/12 home or away kit, printed with the names of the departed players, from either the Everton One or Everton Two stores in the city or did so from the club's online store can get their money back if they can provide proof of purchase.
The deadline for the refund offer is September 30.