It made sense to me: I hate it when there are grounds in my coffee. Ingesting that can't be good for your intestines! And then you try to spit them out, but they get stuck all over your tongue. Yuck.
I've had several arguments over these lyrics. I was so sure I was right. However, the Internet proved me wrong.
I think Ms. Simon should change it. And probably, performing live, she has improvised and improved the song with the word "grounds", for it makes much more sense; and I'd be right!