I have built a few kit rifles, including the TC Hawken models. I have also reworked quite a few. You have not specified which screws as there are more than one thinks. Yes, it probably is a kit as you mentioned the prefix of "K". I have only seen one other kit gun that did not have the k-prefix. I have also seen kit guns that were finished better than factory, but not many. Kit guns are usually very easy to spot. ...
There are many ways to fix that stripped hole and the last one I did, was on the trigger guard. Not only was it stripped, but dry-rotted and I really wound up with a big hole to fill, with real wood. Toothpicks and glue work fine but don't crowd your screws and the wood will only compress to a point. I have also used excelsior with glue. One smith I know, just uses wood with no glue. I do prefer glue. ..
Be Safe!!!