I'm not an expert about this but it's my understanding that all of the messages are stored on Google's servers and we all simply view them. The entries are not being downloaded to your computer and they aren't taking up any of your storage.
I occasionally will search through all these entries to find information about a particular species or birding location. Very handy.
So you don't need to delete anything and I don't think you would want to.
Happy to be corrected on this with better information.
Carl Bendorf
Longmont, CO