After a month, the area would probably heal up with no complications. It may be what foofoo99 indicated, which is a bony spicule (small piece of loose bone) poking out and may be causing some discomfort or there is a part of your jawbone which is sharp and is causing some discomfort. It would be best to go back to your dentist to see whats the best solution.
I am not the presiding dentist, what you are seeing, a straight line, that has not healed, most probably is not the initial cut done by the dentist. It's the edge of the jaw bone protruding out. In some cases, when you have a very irregular bone next to the extraction site, especially very thin bone, after an extraction, it becomes like an edge of a knife, and will cut through. It happens, and if that is in your case, the dentist or an oral surgeon, needs to round the edge of that bone , it will then heal. It usually appear on extractions of lower wisdom teeth, on the tongue side, the bone there, can be very thin.