Apologies for any confusion. The 6-1/4" dimension is the distance from the wall to the end of the post of the double towel bar which is called projection. This is sometimes needed to understand if a door will clear or if it will fit in a particular space.
The surface is fine with texture provided it is not a dramatic plane issue.
If you are relocating any item you can purchase additional mounting hardware kits which include the adhesive tubes. Note the adapters are single use only due to the pre-set foam ring and patented breathable adapter which allow for accelerated curing of the adhesive. All replacement components are offered directly on our web page.
This is not designed for use on drywall, painted, plastered or wallpapered surfaces.