how big is the hole??? pic???

if you are queasy.. hire an exterminator ...

most are night animals.. hiding by day ... set a trap facing in in the evening.. check it the next morning ...

repeat until you are successful.;. or it leaves because you are interrupting its peace ...

in my area.. possum.. skunk... groundhog.. etc ... rabbits take advantage of a prior hole ...

do something before momma has kids.. and then you have multiplied your problems ...

google trappers in your area or zip code ...

your gazebo is yours.. not a disney movie...

ken

You could try trapping as Ken suggests and then comes the problem of what to do with what yo0u trapped. In Michigan transporting wild animals without a state license is illegal.
You could also try repelling the animal by placing saucers with Ammonia under the Gazebo. Easier, in my estimation, then trapping.

yeah.. i meant to come back and mention that.. lol ... thought about that about an hour later ...

hence the referral to a trapper .. who has permits for such ... see link ...

its really all about how hard you want to work in dissuading them ... versus damage.. etc ... some times i get lucky.. and they go away.. if i go out there daily.. and irritate them simply by being around [filling the hoe.. putting down hardware clother.. etc ...] .. some like privacy .. lol ...

as compared to other things.. that can do significant damage.. and need immediate results.. like when momma and 3 raccoons took up living in the eave of my pole barn ... i had no sense of humor about that ... and OMG.. the stink ....

many options.. for you to choose from ... but you have to start.. by figuring out what it is ...

ken

Here is a link that might be useful: link