I don’t think I’ve seen any way to track who is exporting data from a grid. However, it’s likely that such feature can be disabled.
Even if we were able to track that, an user could easily just take a screenshot and thus copy the data without being caught.
Perhaps the reason why you need that is because some user exported and shared data that should not be shared. My suggestion is to lock access to certain applications thru security, so only trusted users would be able to open those applications and thus see sensitive data.
Also, block data browser as well otherwise users with a few more skills would be able to inquiry the data straight from the table.