A renter who pays on time and is pleasant to have around is gold. You’ll find out if she leaves and someone else moves in with no dog, but who doesn’t pay on time and isn’t pleasant to have around.
Don’t make a big deal. Let the lawn mower do the work of picking up the stuff. Thats why lawnmowers have grass catchers. And if it doesn’t have a grass catcher, there won’t be much there to worry about after you mow anyway.
Buy her a pie from a pie house and apologize for making a big deal out of nothing.
If a tenant does not pay rent then they get EVICTED!!! rule #4 before you become a landlord memorize eviction laws in your state and determine the costs.