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.
