Update:
They do, somewhere on that site, provide a Help page.
I ended up calling the tax office in the US to ask if they needed a new agent's letter. they didn't; they did however require a new ID. They did not accept my ID card, which they actually had in the original, and which is identical to my passport and just as valid in the EU. I wasn't going to send my passport to the USA, so I got a notarised copy. With an apostille. You can get those from any public notary in the UK; the one I used a few months ago cost £5. The one I got yesterday, in Germany, cost EUR 11.
(Incidentally, I had to take the notarised copy to the County Court to get it legitimised and get the apostille; it happened to be in the very same building that was once my employer, the very same room in which I met my husband in 1983, the very same employees who recognised us at once and had a nice chat with us. (The Bezirksrevisor, Herr Stark; he used to check our accounts, and as I am not good at bookkeeping, I used to live in quaking fear of him. Turns out to be a really nice, friendly man who remembered my maiden name and lots of stuff I had forgotten. So it was a nice trip down memory lane!)
Anyway, for the future I would advise anyone needing an ITIN to send a notarised copy rather than the original; the price is about the same as for recorded mail and it's probably quicker than going to the Embassy yourself. IMO.