GIMP is something that I use for about a week or two every other year,
but in my experience, if you start with a JPEG, you don’t have an Alpha
layer in the file, and deleting gives you white. You have to do:
Layer->Transparency->Add Alpha Channel
This will add to your existing layer of colors a new layer of
transparencies (from totally opaque to totally transparent). Once that
new layer exists, deleting something will leave you with transparency
instead of white.
You can’t save it as a JPEG with the transparency, because JPEGs don’t
recognize the concept, but you can save it as a GIMP file (.xcf), or
export it as a PNG file (.png) or a lot of other things.
--
John W. Kennedy
"The blind rulers of Logres
Nourished the land on a fallacy of rational virtue."
-- Charles Williams. "Taliessin through Logres: Prelude"