The fallback function may receive additional data (exposed in msg.data). How can I send a transaction with additional data in Remix?
I do not believe you can send data using Remix at this time. What you can do is use Metamask to perform the same action.
If you are calling the fallback function, then you can simply open Metamask, send a transaction to the contract, and include the data in the
Hex Data field of the transaction form.
You can use other clients like MyCrypto as well, but I do not believe you can perform this action in Remix.