How do I turn off the Safari pop up that shows what another laptop is browsing?

Hey everyone, sorry if this is a very poorly detailed explanation but I’ll try my best:

my MacBook Pro will often have a pop up displayed at the bottom left corner of the dock with a safari icon that shows what my moms browsing on either her phone or MacBook. I often click on it by accident and it hands off her webpage to my MacBook. Is there any way to either completely turn this feature off? Or at least make it so I can point it to only my iPhone instead of both of her devices?

thanks!