Even a quick runner can cause brown patches where his feet touched the ground. You can usually remove small children's footprints by scarifying quite easily. The gaps will fill in quickly by new growth and if necessary you can simply sow a few more grass seeds.
You can cut out larger brown areas using a flat spade, loosen the ground and transplant some turf. Probably it´s not worth buying rolled turf for this issue. Simply take a few square centimetres of grass from an edge where nobody will notice. Larger grass renovation jobs - or even complete re-sowing - may be necessary if you are fighting weeds. But this is a lot of more effort.