I believe you will need a letter from the Thai military stating that you have finished your Thai military service or are not required and as such you will not be called upon in the future. This will then need to be translated with the appropriate stamp.
Actually I’d say the check in agent is correct to ask. I also think they meant make sure you have 20k baht or equivalent in cash. Remember if immigration refuse you entry and decide to use the 20k rule it’s the airline that’s subject to returning you to the country you came from. So in essence if they (airline) want to check everything is in order they are within there rights to do so.
As others have said youve overly used the visa exempt and as such need to look at a non o etc.
it’s more about trying to stop the scammers and fraud. Unfortunately it will catch ordinary people out too. I only put my number in my name last month as it was in my wife’s name.