Spell-check is no help here and neither is context, because both words turn up in the same professional register — legal writing, consulting, technical documentation. "A discrete enquiry" and "a discreet enquiry" are both plausible phrases with completely different meanings, and only one of them is what you meant.
An adjective meaning careful, tactful, unobtrusive — not drawing attention.
An adjective meaning individually separate and distinct.
Quick way to remember
Look at where the "e"s sit. In "discrete," the two "e"s are separated by a "t" — and the word means separate. In "discreet," they sit together, keeping quiet side by side.