Holding on the speech bubble on the left brings up a hand, then you can physically shove away the plate. Do you think there should be additional indicators or maybe a mention in the tutorial? This isn't the first time someone has asked that.
I also very much struggled to understand how to clear the plates at first. And even once I noticed the hand going up it took me another 20 seconds to understand I had to swipe. I got it eventually, but a little extra cue might be a good idea to add. This was a joy to play! Thank you for sharing it with us!