You know, I think this is a case in which I would personally just take care of it.
Even if you can manage not to take care of it and manage to get the tenant to do it, you really don’t want to leave this particular problem in your tenant’s control.
The last thing you want is an infestation (which would persist, if your tenant gets fed up and leaves)…
You mention “apartment”, which means if it gets bad, it could end up going into other units…You don’t want to be on the hook for that either (though it would be interesting to prove)…
This is one case I’d say, bite the bullet and take care of it.