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.

thanks

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