What is the white film after soaking in TSP?

I soaked my brushed brass-look cabinet handles in TSP (trisodium phosphate) to get rid of a significant build-up of grease and other grossness. Worked like a charm. But as they’re drying, there’s a white film that seems to rinse clean and come off when I use a brush on them, but comes back again after they dry again.

What is this stuff?

Could be a varnish or laquer. Brass is often treated with such stuff to keep it bright.
The white might go away if you let the pieces dry for a day or two.

Or you might have etched the brass. I dripped some TSP onto my fireplace while prepping the walls and the same thing happened. I attacked it with Brasso, which helped somewhat. But brass is coated with something to preserve the finish, and I think the TSP removed it.