Yes, they control for various variables that they know about. I’m not convinced this gets rid of the bias (e.g. they don’t control for working from home, many others). It is not true that they discuss this obvious objection in either 2.4 or Table 1. They only discuss methods they’ve used that very partially mitigate the issue, without mentioning the problem.

How/why do you think working from home would affect the results of the infected and not infected group? We can throw lots of possible ways to divide the samples of course, but I'd like to understand why you chose that example. (and what's the threshold for "they should've mentioned criteria X")