When using Textools in the UV editor, you get an orange selection box around your selected sub-objects.

However, you cannot select/deselect anything inside that selection box once it's inside the box. Is there any way to disable this box all together, or access the vertices/faces inside the selection box? As is, it makes TexTools unusable...

maybe what you mean is that by default "select elements" is enabled with TexTools- which means that if you click any shell, polygon etc. in the viewport it will select associated element polygons with it in 1 click. It can be changed in the right stack of the UnwrapUVW settings.

If its not what I just described maybe post a screenshot so I can better see what you might mean.

I think he's talking about the transform gizmo, that lets you scale, move and rotate without switching tools..
Just select the move/rotate/scale tools in the top left-hand corner and you'll lose the bounding box around your selection.