For Google Analytics, I had to prove that I owned my domain. I added a TXT record to do this. I also had to prove to Microsoft that I owned my domain by uploading a file (BingSiteAuth.xml) to my site.
Now that I'm up and running with Analytics and Webmaster tools for Google and Bing, can I remove these verification records, or will that break analytics? Does leaving the record and file there pose any kind of security risk?