Can't say I've ever heard "petty negligence" used- which doesn't mean that it does not exist, of course.
Nevertheless, I would just use "negligence", as opposed to "gross negligence".
Either you act intentionally, in which case it is a deliberate action, not a negligent one, or you don't.
If you don't act deliberately, but you overlooked something, or at least did something you ought not to have done, you have acted negligently. Full stop. If you did not check & double check everything to the required standard, then that is negligence, plain and simple. (and nothing petty about it in my view)
If the negligence is such, that it is not just an understandable oversight, but an action that is so negligent that it is almost impossible not to have been aware of the fact that you were acting negligently, then we have gross negligence.
I agree, that negligence might be moderated in a given context ("ok, so I acted a little negligently there, but no harm came from it, right?") but I am not convinced by a separate entry for "petty negligence".