There is nothing from Barrett that weekend, that month, the rest of 1963, during the investigation in 1964... or any time during the decade of the 60's or the 70's where Barrett ever mentions any wallet at all.
The same can be said for Westbrook and/or Owens.
There's news footage of police officers inspecting a wallet at the Tippit murder scene.
Also, didn't James Hosty corroborate Barrett's claim in one of his books?
As for Barrett not speaking on the issue for decades, bear in mind that most of these bureaucrats involved with the investigations weren't willing to risk their careers by blowing the whistle on the problems with the evidence. Being a government whistleblower usually doesn't end well. To that extent, it makes sense why some of them waited until retirement to speak more openly about weird things they observed.