I've used both the AMOS and A-Shell implementations of ZTXFER (on AMOS, Linux and AIX servers) with both ZTERM and ATE clients on Windows 7. So I'm pretty sure there's no fundamental obstacle.
ZTERM doesn't offer the range of client-side debugging options that ATE does, so I'm not sure how to attack it directly, but I would experiment along the following lines:
a) Is it just ZTXFER.LIT? Or is it FTP? (For example, can you FTP using the menu interface, bypassing ZTXFER.LIT?) If so, then I would suspect something about the ZTXFER ESC sequence being filtered/garbled. Try switching ZTERM between 7 and 8 bit modes to see if that has an effect. Try switching the terminal driver. Try sending the ESC sequence "manually" in a BASIC program. Try other ZTERM ESC sequences.
b) If the menu-driven FTP doesn't work, try to determine if the issue is ZTERM vs some other FTP client. Try ATE. Or try something like FileZilla. If those work but ZTERM doesn't, it sounds like some part of the ZTERM/FTP tool chain is broken. (In the old days, the standard recommendation for that was to do a Windows update, and/or reinstall IE, since I think ZTERM shared some network components with IE.) I'm not sure what FileZilla uses, but ATE and ZTERM have separate FTP implementations, so if one works and the other doesn't, it points the finger at some DLL or other Windows-provided component used in the ZTERM FTP.
c) Can you FTP with ZTERM from one of those PCs to some other server? If the ZTERM FTP was broken or blocked on the client side, it presumably wouldn't work for other servers either.