As a writer, supposing this is your scenario, you know better about a larger context. For example how many Mary are you going to bring on the stage? If there's only one Mary, then that Mary was screaming and didn't know what to do when chased by mice. In this case you should put a comma as the relative clause is non-defining.
If you are talking about more than one Mary, then the one you are talking about is that Mary that was screaming and didn't know what to do when chased by mice. In this case you shouldn't put a comma as the relative clause is a defining clause.
This said, only the writer knows what they really want to convey to the readers, and it's up to their pen whether to put a comma.
Consequently, a comma, to an educated reader will change the meaning of the sentence.
Let me give you an additional example:
People, who are found without tickets, will be fined.
Here, as everything that's between commas can be stricken, the sentence reads:
All people will be fined.
But deleting commas:
People who are found without tickets will be fined.
Here, obviously, only the people without tickets will be fined.