That's what I meant, yes!

I always have a hard time with this one because, in French, it's not a towel that is thrown: https://en.wiktionary.org/wiki/jeter_l%27%C3%A9ponge

The French version version naturally comes to my mind, even when I'm thinking in English, and then I can't find the translation because it's too close, yet so different.

I mix up "throw down the gauntlet" and "throw in the towel" at least monthly, don't worry.