Chisel off the old mortar very carefully. Not only will an acid solution not remove blobs of mortar, it will etch the marble badly, leaving it difficult to clean properly and with holes in it if you leave it in contact long enough. Be very sure that your brackets are sturdy enough and are fastened into the studs. Marble shelving is quite a bit heavier than wood shelving.

other than chiseling there is no simple solution.

Alright, then, chiseling it is. Any suggestions on what sort of chisel to use? What sort of surface should I place the marble on when I try to chisel it? Something to absorb some impact? Wood?

Don't worry, we'll be sure to screw the brackets into studs. And these are beast studs, too. We tore through the plaster on the other side, and these are very thick, oak studs.

"other than chiseling there is no simple solution."

You can also just cut off the edges.

Marble is not as hard as granite (or any number of other stones) and carbide tooling with water is often adequate.

If you start chiseling, you're going to find out right away if they are sturdy enough to be shelves. Shocks from chiseling are going to be a good test.
Personally I could not see a marble shelf narrower than 8" having sufficient strength to support itself for very long, let alone any weight. Marble lacks flexive/tensile strength unless reinforced by "rodding"..
I think a diamond grinder wheel would be the best removal method.
Acid will eat marble faster than mortar.
Casey

Oooh. Sounds like a lovely find. Personally? I would only use one tool for the job-- my husband.

Here is a link that might be useful: We too have a crumbling abode

Get an old wood chisel, or a stonemason's chisel. It should be dull, but with a nice beveled edge.

Also get a small iron hand sledge - 2 or 3 pound will do.

Hold it loosely in your hand at a very shallow angle (almost parallel to the marble) and tap it from bare marble into the blob of mortar. Vary the angle of the chisel if nothing happens.

If you are lucky, most of the mortar will pop off.