Fracking, which extracts gas from shale rock, stopped at the Lancashire site after a 2.9-magnitude tremor in August in August.
Cuadrilla boss Francis Egan said no "major damage" had been reported by locals near the Preston New Road site.
But he said residents would get a few hundred pounds each to help with any redecorating.
A number of earth tremors have happened at the site since fracking began in Little Plumpton in October 2018.
On 26 August, residents reported being woken up by the 2.9 magnitude quake, which is more than 250 times bigger than the 0.5 limit placed by government rules.
The controversial process was suspended indefinitely and Cuadrilla said it would repair any damage.
Mr Egan said some "obviously egregious" claims had been sent to the company.
"Lots of people have showed us cracks with weeds growing out of them, for example, or cracks that - when you look on Rightmove - you can see the exact same cracks in photographs taken well before the tremor."
He said reports of damage were in the "low two figures", adding: "It would be impossible to say if that was caused by the tremor, or is it just natural settlement in the building.
"But we do want to retain goodwill, so we will make some payments."
Residents would be paid a few hundred pounds each to help cover the cost of redecorating rooms where plaster work had cracked, he said.
Read the full story here.