Old roots a problem for pool?

Hi all,

I'm just prepping the ground for our 20ft Intex XTR and I'm finding a lot of old decayed roots when pulling up the grass.

Turns out the neighbors used to have a huge tree right at the edge of the property, so a lot of the roots came into my yard.

I'm also limited by our septic field, so moving it somewhere else is not an option.

Do I just rip them all out and fill with new soil? From what I understand I shouldn't add any soil and just dig down because of settling. If I keep digging down I guess I'll just keep finding more roots.