Paine, who recently sparked controversy with a harsh remark directed at England's touring team, is hoping to play for Tasmania soon after beginning light training.
Smith was caught on stump camera trying to remove Pant's guard during the fifth day of the third Test at the Sydney Cricket Ground (SCG)
A video has emerged of a stump vision camera where Smith is seen rubbing the pitch with his shoe spikes, which many purported as him removing Pant's batting mark.
Australia skipper decided to walk back to the dressing as umpires called the end of the second session after Cameron Green, who scored 84, got out.
Apart from the two Tests of the four-match series, Warner had also skipped the entire ODI series after picking up the injury during the T20I series against India.
Aussies drubbed Kiwis by 279 runs in the third and final Test at the Sydney Cricket Ground, thus concluding with a 3-0 whitewash.
There was talk about Paine's captaincy after he had said that this could be his last summer. Paine took over the reins from Steve Smith after the latter was banned for a year.
Tim Paine expressed his discontentment after getting out by a controversial DRS decision and then seeing Ross Taylor getting saved by the TV Umpire.
Cummins on Thursday became the most expensive overseas buy and the second most in overall auction history of the Indian Premier League.
On Saturday at Adelaide Oval, Warner was batting on 345 with Australia cruising on 589 for 3 when Paine declared the innings before wrapping up the visitors on 302 runs and asking them to follow on.
