I think you missunderstand. If the llm can "add back" 200 bits of information, these 200 bits are superfluous by definition.
They can quiet literally be inferred from the starting 300 bits. And the llm has proved it.
If the receiver wanted these 200 added bits, she could infer them either herself or even use an llm to do it.
If the receiver wanted these 200 added bits, she could infer them either herself or even use an llm to do it.