Thank you for the transparency and stepping up to reimburse!
The most straightforward flow would be sending eth to Lido Execution Layer rewards vault 0x388C818CA8B9251b393131C08a736A67ccB19297 (can be checked here: Mainnet | Lido Docs) By this, the funds would get accounted as regular Execution Layer rewards and distributed to stETH holders during the next day’s oracle report. I must note that this way the distribution would include the protocol fee of 10% – again, just as with the regular rewards.