First off it only scans browser addons/extensions by matching them to known browser ids.
Second this has nothing to do with home lab or network so nothing to secure there; Either dont use linkedin, use a firefox based browser or, if you read the actual browsergate website, changing your user agent to anything not chrome/chromium based should block the script from running as it runs this check before anything else, or just dns block 'linkedin.com/li/track' iirc to prevent from being sent back or do all of the above.
Yes this is a volation of privacy but helping push the framing around this thst it scans your computer with that terrible title isnt helping the situation.
Edit: spelling