Karl Wolz and I have established that on an iPhone you can select
desired text in a message before hitting Reply, and (only) it will be
quoted in the resulting reply.

That's a method used in many email programs, so it's certainly worth
trying on your phone.

I've just now briefly tried it with gmail's web interface, where it
seems not to work.  There you have to click the three dots at the
bottom left of the compose pane to expand the quoted text, and then
remove the parts you don't want.

Yours,
David