Zampa's team mates Steve Smith and David Warner have just returned to the national setup after serving 12-month bans for their roles in a ball-tampering scandal in South Africa early last year.
"I haven't seen the photos, but I know that he has hand warmers in his pocket," Finch told reporters. "He has them every single game he plays.
"I honestly haven't seen them (the images), so I can't comment too much on it. But I know for a fact that he has hand warmers every game."
Australia next play Pakistan in Taunton on Wednesday.
(Reporting by Rohith Nair in Bengaluru; Editing by Peter Rutherford)
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