The agent is not a guest. She has a signed agreement from the seller to be there. Anything that agreement does not specifically exclude, and is otherwise legal...
So............if one does not explicitly prohibit an activity(s) in the listing agreement an agent can do whatever they want in your home?
To clarify further. I've been to more than a few open houses in the last two or so months. Some of them are new construction. The builder is the owner. I don't really consider them "homes". Obviously no one lives there. Others have owner occupants that have moved out, lock, stock, and barrel. Completely empty. They're not likely to be back until closing, or maybe not even then. Some of the houses, the owner has moved out, but left some furniture, but nothing else. Either the owner hasn't gotten around to moving it yet, or they're going to sell it. Ive also been in a few where the owner is still living there, but obviously left during the open house. Leaving an agent there. Now you could say, common courtesy might require you to ask. I wouldn't argue that. Ive been carrying every time. Never gave it much thought.
As far as the agent is concerned in the OP. She has a signed agreement, giving her permission to be in that property, anytime during business hours. The owner has 3 ways to prohibit on the property. By specifying in the agreement. The owner can add that in. By posting posting a compliant sign on the door. Or verbally telling the agent. Any one of those three, or combination. The agent must comply.
If not I believe she is on pretty solid ground legally. For FOID carry. Or better, CCL. Just my opinion.
Female agents have been murdered while alone at open houses, or with a client. If an agent wants, and feels the need to have the ability to defend themselves, and have not been specifically prohibited. I would say alive is much better than dead and legal.