I believe you should be able to long-press the suggested word and it'll give you the option to delete it.

I run into this all the time as well. It knows that if a new line starts with "M," I'm probably trying to start typing "Matt" for my signature. So I choose "Matt" from the suggestions and it then suggests "Damon"

But it hasn't done that since I removed "Damon" from the suggestions.

I've been using Swiftkey since it was in beta on the phone and the same thing on the tablet. It's easily my favorite replacement keyboard.