First, ask yourself how much you want to keep this painting, and if you're willing to go through a little hassle. If the answer is yes -
Stain blockers such as BIN are just white-pigmented shellac. Buy some clear shellac, a roller applicator designed for applying shellac/polyurethane, and the finest grit sandpaper/sanding sponge available. Make sure your painting is dry before beginning. Apply a very thin coat of shellac to the painting and allow it to dry. After it dries, apply another very thin coat. You want to avoid any "row-marks" or bubbles, and you want to make sure you fully cover the painting with both coats of shellac. After the second coat dries, LIGHTLY sand the entire surface - when I say "lightly," I mean LIGHTLY. After sanding, take a slightly damp lint-free rag and wipe the surface to remove sanding dust. You should have a clear base coat of shellac which you can then paint over. The marker shouldn't bleed through.
