A not (yet -- ha ha ha ha ha.... I know it's PC to say it that way, but really, she's not likely to change at this point... sigh...) frum relative was once spending Shabbos with us and went to wash the dishes after lunch. Of course we told her very nicely that we don't wash dishes on Shabbos. She was, equally of course, incensed. "What!? I can't do the dishes?!? This is crazy that I can't do what I want!" I couldn't help thinking that her teenagers had probably had a similar fight with her a few years earlier. "What!? I have to do the dishes?!? This is crazy that I can't do what I want!" Mercifully, HaShem held my mouth shut; there are just certain things a son-in-law shouldn't say. Whoops... I kinda outted that one...
One of the other crazy restrictions we have is that we are not allowed is launder. It turns out, though, that it can be more difficult than you might have imagined to avoid doing laundry. The source of the difficulty is the ma'amar Chazal: shriyaso zohi kibuso/soaking is laundering. (Google translate rendered, "Mining identical Jebusites", btw. Buyer beware.) That is, sometimes just getting a bit of cloth wet is considered laundering it. The Mishna Brura, in one of his famous and essential introductions to a topic (Siman 302, sk 39) give a summary of the issues.
The most lenient explanation of that statement is that simply pouring water onto a dirty (not just dingy, btw, but actually dirty) fabric, e.g. a garment, tablecloth, or the like, with the intent of cleaning it is the malacha d'oraisa of of laundering. Pouring water onto clean fabric, however, would not be a problem mi'di'oraiso as long as you don't squeeze it or scrub it. It remains, though an issur d'rabanan as a hedge against coming to squeeze it.
The next step up is to consider even pouring water onto clean fabric to be considered laundering. However, that is only if the pouring is done in a cleaning manner. If, on the other hand, one is getting the fabric wet as part of cleaning/drying something else (derech lichluch), then there is no problem. That's the heter to dry your hands on a towel. Your intent is to clean your hands, not wash the fabric. It is worth noting, however, that if your hands are cleaner than the fabric, one could still run afoul of the laundering issue. (It's that old "be honest" thorn in our sides. I know you thought you could be sneaky by getting your hands really wet and then drying them on a dirty tablecloth; but HaShem is on to that one also.)
The most stringent opinion is that even drying your hands on clean fabric is a problem if there is a lot of water. The Mishna Brura says it's worth paying some attention to that opinion, so you should shake excess water off your hands before grabbing the towel.
By the way, there were lots of other times that HaShem didn't clamp my mouth shut. It's times like those that I think free will is overrated.