It seems like you can interpret 'check your privilege' in two ways, really. There's the idea of turning the mirror on yourself and self-awareness. But you could also interpret the phrase more literally: As though, by acknowledging privilege — like a white feminist calling out white feminism — you can somehow literally check it, as in take it on and off.

"Just because you acknowledge privilege doesn’t mean you neutralize it, or that you shed the lens that comes along with the perspective. I wrote about these sorts of 'awareness disclaimers' that are found in feminist essays these days, especially ones by white women, though not necessarily exclusively by white women: There's this passage in each one of privilege acknowledgement. It's understandable, why it's there; for one thing, if that passage doesn't appear, it will be pointed out by the readers in the comments.