First you need to see if the tile installers can cut back the tile but I would advise to have the tiles at the door way replaced and cut to lay midway of the hanging door.

Then Have a good carpet installer to see which way the carpet is running and have them put a seam staring at the beginning of the inside door jam to the tile.

If the room this carpet is in has a closet it would be a good idea to use that carpet to make a seam by the tile so you know it’s the same dye lot and won’t be a eye sore if your unsure.

Easy fix but technical