The first is that who decides what is a "green miner" and who isn't. That's right, they have centralized entities doing that which means the mining process becomes less decentralizedd as the process can be hijacked to exclude miners they don't like.
Proof of owning your solar panel or whatever and a contract in which you;re liable for damages if you breach it by using grid power.
Prett easy to do and enforcable.
Second, who actually guarantees that any of the transactions are going to land in a block. This would require all miners not submitting their block templates to Bitcoin and to the centralized entity. This stinks of sanctions.
You simply broadcast them to the mining node, the other nodes\pool don't know of their existence, the green mining pool finds a block, adds them and the block is valid by all means and will not be rejected.
Nothing extraordinary in it, some pools do this with their internal transactions too.
But the thing is that you can't mine without a grid, and qualifying as a full green miner unless you sue some hydro plant would be impossible, all the big guys use coal and gas and maybe nuclear but nobody is going full green, it's simply too expensive.