Make sure you’ve tamped or rolled the soil. Just tossing dirt in a hole does not fill it, next time it rains it’ll settle and you’ll get a big muddy dip in the yard that nothing will grow in.

In terms of covering it it depends on where you are located right now. It’s really too late to plant grass seed in most of the cooler areas of the US (it needs about two weeks to sprout and another couple weeks to establish before a frost). Looks like it may be warmer there so you may be fine. A bag of local grass seeds from the big box store, put it down a bit heavier than the instructions and lightly rake it in. Cover with straw and keep damp until it sprouts, after about two weeks after sprouting reduce watering to only a couples times a week to promote deeper root growth.

It’s also worth figuring out why your dig dug the hole though, otherwise it’s likely they will just do it again.