Another Newbie needs help with line tool

I tried searching for the answer but what I’ve found wasn’t in depth enough for my question. Bear with me, I’m new to this. I can’t for the life of me figure out how to “smooth out” lines. I did the “Image Trace” around a pattern I had cutout by hand. My issue lies in the fact that the software imported quite a few “glitches” around the perimeter. I’ve tried adjusting the points, but I don’t know that I’ve grasped how the “curved” works. I’ve attaching the image in what should be a gentle arc that has all these additional points the tool added that I simply can’t figure out how to eliminate. If I try deleting points, I end up with a straight line. How exactly do the 2 “boxes” work that show up on curved points? That’s the source of my struggle, I believe.
image

see if this helps

Pen Tool in Easel: Ampersand Project (youtube.com)

Well tried you are, really diving into vector editing, and that can be tricky at first! It’s great that you’re trying to smooth out those lines after the image trace.