the word "anonymity"
And I think they quite like the anonymity that provides them.
What is" anonymity that provides them"?

Question

Answer

Did you mean the "anonymity that IT provides them?"

That would mean they enjoy how "it," whatever that is, allows them to be anonymous, or unknown.

For example: "The girls enjoyed how their masks provided them the anonymity to talk to whomever they pleased."

That is, the girls' identities were unknown, therefore, they were anonymous and could act however/talk to whoever they wanted.

Answer

thanks

Answer

Take another look at your sentence. There's something not right here.