Hi Kara, Care.com only sends your references an email at the time that you add them. This email lets them know that they can write about the work you've done for them and have that blurb posted on your profile, this way future employers can see what they have to say. If they are receiving multiple emails, it may be because you have entered them as a reference on multiple service profiles. If this is not that case, feel free to contact Member Care so that we can look into this further! We can be reached at 877-227-3115 or you can message me here.

You have to go under references and delete the referenced forwarded on the page.

Honestly Cara, I feel as though that care.com should no longer be worth your time. I've not used this site for too long so honestly I have no idea. But if you want reliable work/sitter you should put your time and effort elsewhere.
I had a bad experience with the sitter I found on care.com and a bad experience trying to find someone to be a sitter for.