Thanks, everyone, for the feedback. I had an email exchange with TravelLink yesterday re: AmEx. They stopped taking it two weeks ago due to fraud and were hoping to be able to work something out with AmEx to add it again.
I asked if there was any way they were willing to take my AmEx, if I sent a signed confirmation and/or a back-up billing method. After checking with their Finance Dept, the representative emailed me back and agreed, as long as I provided a back-up card, full address and phone number.
I found this to be excellent customer service.
Susan