Q. Does it matter if they have or had presence there (Columbus)?
A. No. It's just a possible explanation for the mistake. A more likely explanation, they (your employer) just don't know any better.
Q. Should I ask for a full refund in Columbus or adjust the difference in rates between Columbus and Grove City/RITA and ask for a refund in GC?
A. A full refund from Columbus. If an adjustment was due (and it isn't), it would be made on your Grove City return.*
* You normally only have to file a return in the city you live in. It is not necessary to file one in the city you work in, if different. Your employer will remit withholding to the city you work in, but you do not file a return unless you're claiming a refund or your employer didn't withhold enough ( both highly unusual). The city you live in will allow a credit or partial credit for the withheld tax you paid to the work location city. Grove City allows a 100% credit up to their 2% (Columbus is 2.5%). But GC may not allow any credit, in your case, since the Columbus tax was (apparently) inappropriate.
