This is very pretty.

This is just my opinion, but I wouldn't worry about the underside. It will never be shown. I wouldn't worry about it.

However, once and a while I do like to hide my stitching on the back side. So I have used iron-on interfacing on smaller items. You can buy it at any sewing store. I bought the very light-weight iron on. It comes in different weights. Back in the old days, when I sewed, we had to baste the interfacing on to our material, for collars, necklines, etc. Today it irons on, just make sure you have the glue side down when you iron it.

I got this idea from others at this blog, so it is not my original idea. It was a great suggestion.

Adele

I also use lift weight iron on interfacing on tea towels, etc.. check you scarf.. is it sheer? you may want to add the interfacing across the whole scarf, if the interfacing will make the scarf dark where you iron it on to cover the stitching.. when I interface towels, I cover the whole backside, not just the stitching.. Hope this makes sense to you..
Happy stitching!

You can just another plain white cotton fabric for the base to cover the back stitching by sewing it around.

and if you like some trimming or lace. Have fun

I do the same thing dye. Love that iron on interfacing.