I am renovating the old lawn. I dethatched the old lawn by dethatch rake and cultivated it with electric cultivator. But some areas still seem have old grass and maybe the root layer (see picture). Do I need to strip that layer off entirely before seeding? I plan to put top soil layer and then seeds with fertilizer.

jz2022, welcome!! That a lot of work that well you didn't need to do. I just spray roundup, wait a few days to make sure what didn't get sprayed shows up. Spray again and wait 12 hours put down a good fertilizer before putting out grass seed.
Fall is the best time to plant a new lawn.

Water it well and wait a week to see if/where grass resprouts from old roots and remove those. If a lot of the old grass roots remain they will resprout along with the new seeds —but if you're seeding the same variety that shouldn't be a problem.

Please don't use Roundup or other poisons, especially at this time of year when bees are working. Nothing wrong with healthy physical activity.

If you want peace of mind, rent a sod cutter and cut that area down two or so inches.

You can then take you electric tiller, loosen the the soil and put in as much top soil under over the seeded area as you wish with very little remnant debris to deal with.

When we seeded an area with scrub sod/grass we alway used our sod cutter to clear the area, far, far less hassle to work with.