The landlord/owner of the home we're renting from has a key lockbox on the door, which I highly dislike. At this moment, we're in a crisis with COVID being a huge problem sweeping the nation. We requested if the landlord can withhold showings at this time during this circumstance. He initially agreed for one week to not do showings. Yet realtors/prospects are still showing up when it is recommended by World Health Organization/Department of Health and Human Services to keep yourself socially distant/isolated. Do I have any legal right to ask them to leave/refrain from entering during this time?
I like Mr. Weiner's answer, which is probably the most practical solution, and it is technically true. That said, a landlord has a duty to keep the premises safe from health hazards and to provide you with "quiet enjoyment," which during these unprecedented times would likely include not allowing others to enter the premises when all health officials are advising against such activities. In my opinion, you're within your rights to refuse entry to realtors/prospects while we're still under "stay home" orders from the governor. This is particularly true if you are in a high-risk category.
Put up a sign on the front door of the house that the house is under self quarantine because of the CV-19. That should discourage most visitors.