No pictures are showing.

Try posting pics in a comment below mine.

6ft. level and tapered gauge

baseboard and tile

between tile joint before grout

grout joint with meauring tape

biggest gap between baseboard and tile

tile lippage

I hope you can see the pictures. sorry Its my first time posting here. Only thing The contractor says needs fixing is to scored out grout by the baseboards then place it with caulk.

and claims everything else with tile install is good. So could scored fix the big gaps around the perimeter joints?

That's a complete do over. What a hack job.

Caulk at the walls while correct (not grout at that location) would be correct it will not address the balance of the hacked up install. Definitely poor workmanship.

not sure if this is the proper method but I used 6ft. and 2ft. level, tapered gauge, flash light, and couple credit card.

Yes, but the image with black L shape ruler is where biggest gap is between the tile and baseboard

Tile and baseboard gap has nothing to do with the tile setter. The baseboards need to be reset. They should have been removed for the new tile. The lippage, grout joints, etc. are where the issues lie not the baseboards.

it was

Thank you so much for the prompt response. They told me no need to remove the baseboards but lot of them did get damaged. The Tile setter install the grout around the perimeter. Today they came and score out at the baseboards in some areas and is coming back to reinstall the towlet and fix baseboards. Is it ok to have grout still along the tile egdes and left in the perimeter joints? This is so frustrating. Also they are still trying to convience me the lippage and the grout joints are fine!

You need to be the one to stop them, and if you need to, take some action, to get this done right. They will tell you anything, to consider themselves done and gone. I suspect, they are not actual tile setters, since this is a really terrible job. Not removing baseboards, is wrong.