At our company on a right seat T/O, the F/O pushes the TL’s to the CLB detent or TOGA. When the FO makes the “Check Thrust” call out his or her hands are to be off the TL’s and the Capt now has the TL’s. (If the FO’s hands were still on the TL’s for a second or two after the FMA’s indicated correctly, I would push his hands of the TL’s and make the “Check Thrust” call out. I have never seen that happen, even as a training Captain, but there’s always a first time I guess)
In normal circumstances, neither pilot is to have their hands on the TL’s from V1 to gear up callout to prevent an inadvertent reject above V1.
If a reason to reject presented itself during the time the F/O hands were on the TL’s the CA is to call the Reject, the FO is to perform the reject until the Captain takes over.
If the FO has their hands in the TL’s after the check thrust call out I would push them off. If the FO put his hands on the TL’s prior to the gear up call out, I would tell him to remove them.
Our SOP are clear on these points. I would ask the OP what is the SOP at his outfit?