[Snake22]

если интересует способ без переобора то через ShellAIP

Код:

function Recycle( FileName: string): Boolean;
var
  FileOp: TSHFileOpStruct;
begin
  FillChar(FileOp, SizeOf(FileOp), 0); 
  FileOp.Wnd := Application.Handle;
  FileOp.wFunc := FO_DELETE;
  FileOp.pFrom := PChar(FileName);
  FileOp.fFlags := FOF_NOERRORUI or FOF_NOCONFIRMATION;
  FileOp.fAnyOperationsAborted:=true;
  Result := (SHFileOperation(FileOp) = 0);
end;

procedure TForm1.Button1Click(Sender: TObject);
begin
Recycle('C:\tmp\*.txt'#0);
end;