You can get a new tailgate without logo for under $200
https://www.ebay.com/itm/New-Tailgat...03ae5724198b31
You can get a used gmc tailgate for half that. Selling your tailgate you have now can get you under $50 out of pocket if you go used, Just over $100 if you go with a new one.
Car-part.com has you covered
And yes it would bother me if someone took the time to convert their GMC to Chevrolet