The elves don't seem to actually do anything beyond get into places and watch people–they don't steal or destroy anything (though they may draw mustaches on any photos they find). They do seem to congregate in greatest numbers where there are secrets to be observed, including secure areas at ADI headquarters as well as the homes of characters who have something to hide. They do seem to be particularly drawn to cursed items and characters with powers, as well as characters who tested the Illumination Rite light strands.

Security footage does not show the elves in full motion. When an elf that's on camera relocates, footage may show the elf moving a tiny bit (little enough that there's always plausible deniability that the cause could have been mundane) before the feed seems to glitch out for a moment and then the elf has simply disappeared or appeared. Neil Grace, head of security at ADI, is very upset about this situation and is one of the voices calling most loudly for a company-wide effort to deal with the elves.

Regarding Ren, she will likely be visible in the rescue location to the rescuers who arrive first on the scene. These individuals will witness her breaking apart into a multitude of insects and scuttling away to join the rest of the swarms. Picking out which bugs are Ren and which aren't will be impossible, but maybe if you just kill them ALL, you'll get her? Good luck, team!