This solution is in the form of step-by-step hints, where you can take as many hints as you need, and stop when you don’t need any more.

Clarifications:
– There is no math
– Anne and Mary’s names aren’t important. You could replace them with A and B, Alice and Bob, however you want.

Answer:

Anne’s birthday must be a good reminder for a phone number. But what phone number could that be?

A local phone number in the United States, where you don’t need to dial an area code, has seven digits.

Therefore, the ‘birthday’ hint that Mary was thinking of must have seven digits. 

What could the seven digits be? A date? No. Since seven digits doesn’t convey a date (in any reasonable format). Plus, Mary doesn’t know the exact day.

Could the seven digits imply a holiday? No. Holidays either: 
 -fluctuate year-to-year– making it impossible to reliably correspond to a birthday   
-correspond to an exact day, which Mary doesn’t know.

Not a date, or a holiday, then. But, some other simple ballpark for a birthday. It must be the month! There’s an additional tip-off for this in the question itself, where it mentions that the birthday was the month before last, implying the birthday’s month is a pertinent detail.

How can seven digits ever imply a month? It can’t be by the number, since that only requires a couple digits. Could there be some other way?

If only there was some way to spell things using telephone digits. But, wait. There is! Telephone mnemonics are a widely-known system for corresponding telephone digits to letters of the alphabet.

Therefore, the seven digits of the telephone number must spell out, with a phone mnemonic, the name of a month.
What months have seven letters? J-A-N-U-A-R-Y, and O-C-T-O-B-E-R.

Anne’s birthday is in January or October. Anne’s birthday was the month before last.

Therefore, the current month is either March or December.
There are no federal holidays in March! But there are in December.

Today must be Christmas 🙂