As a reader, my first choice would usually be to take whoever is subject of the main clause (Alice) to remain the subject in the following clause; but I could never be sure, and it might be ambiguous in many cases. There is no real solution. The only way out is by recasting the sentence such that the right reference will become clear from context. You will usually need to make it longer by adding more information:
Alice reminded Carol about how she helped with Carol's paperwork last week.
I agree that this isn't the prettiest of sentences, as using the same name twice in a sentence is usually not done, but it might be acceptable. If the reader knows that the paperwork must be Carol's, references will be acceptably clear without Carol's:
Carol seemed fairly happy now that she didn't have to worry about the documents any more, but she failed to mention payment. Alice reminded her about how she had helped her last week with the paperwork and requested a share of the proceeds.
A sentence rarely comes without context: usually you have something to work with, and often things will naturally fall into place even with several persons of the same gender.
Note that the problem is also very real with two or more inanimate objects; it, that, etc. can often lead to similar ambiguity:
The difference between Rome and Carthage was great; its economy also depended very much on trade, and yet its merchant class was far less powerful than one would have expected.
If I changed the first sentence so that Rome became the subject, I believe its would logically point toward Rome first:
Rome was very different from Carthage; its economy also depended very much on trade, and yet its merchant class was far less powerful than one would have expected.