Threshold bar and there are a lot of nicer options than the one you have pictured. You could get a larger nicer looking one that would hide the poorly trimmed edge. It's not rocket science to fit, just trim to length with a junior hacksaw.
You can pull the carpet out with a screwdriver and you'll probably see how it's fixed to the floor, push it back in with a screwdriver or pry bar preferably.
There are specific types for that. Topps tiles do some reasonable ones. I've custom made solid oak ones when it's difficult to find a ready made alternative.
I've just had a similar thing. The guy who is tiling my hall said he would include fitting a wooden 'threshold' to bridge the gap from tiles (higher) to wooden floor.
It became a non issue in the end as we found thinner tiles but he showed me examples and it looked fine.
Threshold bar and there are a lot of nicer options than the one you have pictured. You could get a larger nicer looking one that would hide the poorly trimmed edge. It's not rocket science to fit, just trim to length with a junior hacksaw.
You can pull the carpet out with a screwdriver and you'll probably see how it's fixed to the floor, push it back in with a screwdriver or pry bar preferably.