Hi there, is that a 1 inch cut tile in front of the door ? He should have installed a schluter to fit the carpet to. When he comes back to grout get him to install one. He could reverse it and glue it down and you could nail a piece of gripper close to it and kick the carpet to stretch it and tuck it between the gripper and schluter . you will have to cut the carpet straight of course.The schluter is designed to protect the edge of the tile. Not very professional on his part. IMHO.

Thanks - I had a feeling something was wrong with this but no knowledge to tell them what to do. It was grouted yesterday and he's gone. :-( It was a difficult relationship with poor communication and I was relieved when they showed up and finished the work at all. (They did wallpaper coverup removal and texturing as well and it was over 2 weeks start to finish!)

Bottom line is - I doubt they will come back and do anything at all to correct this so I am stuck with dealing with this on my own in all likelihood. That's why I was asking about something glue down I could just add on top - like a "T" molding.

I suppose the only "right" way is to take out the last row of tiles and put in one of these fancy transition pieces - http://www.schluter.com/137.aspx -

But that's going to cost me a lot to get someone else to fix it - and we already went way over budget - so I'm just hoping for a less professional but functional DIY solution. :-/

You dont have to take out the last row to install one instead of the schluter being installed under the tile you reverse it and install it under the carpet tight to the tile. ( you have to clean the edge of the tile ). Although you would need someone with a bit of expertise to fit the carpet properly. There are rubber or vinyl T moldings that you could use like you mentioned , They will work fine . However part of it will sit on top of the tile raising the profile and creating a tripping hazard . It will be a small hazard but never the less it is something that if you can avoid you should.Go to a local carpet or flooring supplier and they should be able to sell you one and as you say just glue it down cut the carpet to go under the lip of the molding.the carpet should be stretched and held into place by a piece of gripper by the molding so it wont wrinkle there. Please use a decent glue or you will end up just kicking it off. Normally you would not put a cut tile in front of a door like that. Sounds like you had a couple of problems with those guys , sorry to hear that.
Good luck

Thanks Blueboy1 - now I understand what you meant about reversing the schluter. This gives me a better understanding of the best way to go - much appreciated!

:-)

Will use a very good glue for sure.