The ICC already has the authority to punish people who interfere with its operations.

It's on them to prosecute people who cooperate with sanctions and the like to retaliate against the judges or lawyers or others working for the court, and they can do that any time they like.

Literally, they can write a warrant for the president of their bank, or the highest Microsoft rep in Europe, or anybody involved in any way, and the ICC-signatory country they're in must hand them over.

They have the authority.