You presume that the concept of a symbol would be foreign to ET. Unless you're in some loop I'm not aware of, I don't think that premise is a given. It seems reasonable to me to believe that a sentient being, even one foreign to the Earth, would understand the concept of a symbol. It is, after all, the concept of symbols that allows for a written language or even speech. 'Dog' is not a dog. It is a word that we who speak English understand to represent a furry creature prone to drool and bark.
What is the difference between the vocalization for the animal dog and the meaning infused into the piece of cloth we call a flag?
I think if aliens were familiar with our use of symbols, they would be familiar with it in a Monty Python sort of way. I can see LGM's telepathically laughing at our funny little dances and way too serious reactions when it comes to these symbols. It's Reality TV for them!