what is support log me in rescue

According to Google, it's "On-demand remote support for help desks, IT, and customer care built on the industry's leading remote control solution from LogMeIn."

Where are you seeing this on your computer?

LogMeIn Rescue is a remote access tool that has legitimate purposes. It is also commonly exploited by criminals who attempt to convince you that a problem exists with your Mac, but it cannot be installed without your explicit consent. Never install anything on your Mac unless you know what it is, how it works, the reason it is required, and how to get rid of it when you don't want it any more.

Read about such online scams here: https://en.wikipedia.org/wiki/List_of_confidence_tricks#Online_scams.

For more information regarding browser popups that won't go away read Phony "tech support" / "ransomware" popups and web pages.

Describe what she did when that happened. Did she grant the criminals remote access to her Mac? That would typically be accomplished by calling a phone number that appears on the Mac and supplying a numeric code they provide.

To find out how it works go to https://secure.logmeinrescue.com/Customer/Code.aspx and click "How It Works". Note what it says:

"Remember, only accept support from individuals and organizations you trust."

Any individual or organization claiming to have found a problem with your Mac via a spontaneously appearing message is by definition not trustworthy.

Dastardly Charlie Brown. 🙂