The phrase "to grab a towel" means to quickly take a towel with your hands. It implies the need to get a towel for a particular purpose, like drying off after a shower or pool.
Sentences with «to grab a towel»
So grab your towel and get your sweet sweaty body moving! (fitbodyhq.com)
No need to pay for a beach chair, just grab your towel and lay down on the beach, and you're there for free. (thebarefootnomad.com)
Don't expect them to hold for so long because kids are not gentle when grabbing their towels. (myquietspot.com)