How effective is tobradex (tobramycin and dexamethasone) treating a chalazion?

Not very: A chalazion is the cystic product of a stye which the body has surrounded with a wall. Tobrex (tobramycin) will not penetrate. You can try heat but if the lesion is obvious, large or bothersome , see your ophthalmologist for correction.

Minimal effect: Tobradex, (tobramycin and dexamethasone) a fine combination product of tobramycin and Dexamethasone for topical use on the eye, will not penetrate into a formed chalazion. This is a cystic wall around the products of inflammation from a previous stye. Heat application in a diligent manner may get rid of the chalazion but some have to be surgically removed in a minor office procedure.