There is no "changing the code". That's not how smart contracts work. The code[1] as it was written and deployed is on the ether blockchain and will remain on the ether blockchain in its current form so long as the blockchain remains existent. It is set in stone.
Brave could make a new BAT token and point their browser to use it, but they don't get to do anything with the original code controlling the tokens everyone is already using. It cannot be disabled, modified, or deleted, by Brave Inc or by any person.
[1]: https://etherscan.io/address/0x0d8775f648430679a709e98d2b0cb...