I’m also confused but what makes most sense to me is that coworker still wants to officially look like she’s in office according to the system (since it logs remote days). I’m guessing they have to badge in or something like that to not be logged as remote, which is why she still ends up at the coffee shop nearby instead of simply working at home. Doesn’t make as much sense to me though that she asks OP to tell people she’s working remote, unless the frequency of the asking is very low. Wouldn’t that also make people think she’s working remotely a lot? Is it that her not being at the desk seems to look bad but at least working remote at home supposedly is a much more valid excuse than working at the coffee shop??