What do you do when you call a business after hours and the Auto-Attendant says, "...Press X for the company directory... type the first few letters of the person's last name....?" Those bots are expecting the traditional letters-on-a-phone-dialpad arrangment (ABC on 2, DEF on 3, etc.). Is there a way to make this work on a 7100?

Alt + Letter key

So to be clear... if I called your office and needed to spell the first few letters of "itmediaco" to reach your extension, I'd type:

alt-I which would send the number 4 tone
alt-T which woudl send the number 8 tone
alt-M which woudl send the number 6 tone
etc...

How does it know when I press alt-I (which is really alt-UI) that I want the I tone (number 4 tone) and not the U tone (number 8 tone)?

You have to use double-tap while holding the alt. It waits 1 or 2 seconds before it will actually send the tone.
SO:
alt-UI+UI which would send the number 4 tone
alt-TY which would send the number 8 tone
alt-M which woudl send the number 6 tone

D'oh! I called one such system the other day and I pushed the buttons without much thought and it did not work! Told the person later that his auto-attendant was not working.... <slap hand on forehead>