How Can I Deal with This Ice Dam as a New Homeowner?

Hey everyone, I'm a first-time homeowner and I've found what I believe is an ice dam forming at the corner where my unheated mudroom meets an unheated sunporch. I'm worried about the damage it could cause, especially since we've just replaced the old, rotted gutters. I really want to prevent my new gutters from getting damaged, plus I'm keen on taking care of this old house to avoid any major issues down the line. Any tips for removing the ice and preventing it from building up again would be greatly appreciated! Thanks!