yes, I do believe it's called a transition strip.
yep, it's under the wall and not just under the base board. The baseboards are already removed. It's peaking out the one side of the wall to much for the trim to hide, so we have to remove it. The wall obviously never used to be there, and I'm not sure why they wouldn't just remove the transition strip first before constructing the wall.

The transition strip is screwed to the floor, not nailed.
Thanks for your help. We tried a second time to push in under the drywall so it wasn't peaking out anymore and we think that will do the trick. He used a hammer and some other flat headed tool. If we have problems when we are laying our floor along that little wall, we will try your ideas.