Agree with Stax. This is a temporary compaction which should fix itself if you do nothing.

I guess it depends on your soil. In my area tire tracks do not disappear. We have to level off with top soil and reseed.

In our soil tire tracks also do not disappear. Do you know anyone with a garden tiller? Once soil dries a little you could till, rake, and seed. Wheelbarrowing topsoil will be a lot of work.

Tire tracks don't disappear around here either. Rake it, smooth it out, or fill it as needed. Some of those spots look more rake-able, but the second photo looks like it might take a little extra work.

If the soil is wet/muddy, you can use a flat tamper to tamp it down. I've done that in the past.