Odo is exerting influence over the rest of the Great Link.
I don't buy that at all. Odo's pro-solid propaganda wouldn't hold up for more than 1 minute in the Great Link. Moreover, Odo becoming a pro-solid propagandist is ludicrously out-of-character for the character of Odo himself.
Realistically [albeit, I must adopt the unrealistic version of the Odo character that the writers themselves also adopted ever since they made Odo jump the shark, which happened when Odo inexplicably agreed to obey Sisko's evil order not to cure the Great Link], the communication would go something like this:
Odo: "Hey! You changelings were all wrong! Solids are kind, loving, wonderful people! Therefore, you must recognize that fact and start loving them all right now, just like I do!"
The Great Link: "Are you talking about the same solids that have just almost caused our genocide - deliberately?"
Odo: "Well, yes, but............um...err...durr...."
The Great Link: "Do you think that kind, loving, wonderful people would commit genocide against our people?"
Odo: "Um...err...durr...."
The Great Link: "Don't you believe in justice above all else, Odo?"
Odo: "Of course I do, that's my number one value!"
The Great Link: "Did you think you were being just when you obeyed Sisko's order not to cure us of the genocide disease that the Federation inflicted upon us?"
Odo: "Um...err...durr........................No, of course I was not being just! I must have been out of my mind! Laas was right! Solids have corrupted me into being their stooge...and even worse, an evil stooge! Please, I beg you to forgive me!"
The Great Link: "Our brother Laas is dead. You killed him, Odo, by spreading the Federation's genocide disease to him."
Odo: "I'm so sorry! I am ashamed of myself!"
The Great Link: "Odo, as a matter of self-defense so that the Federation never again has the chance to annihilate us, we will be regrouping and launching round two of our war. Are you with us or against us?"
Odo: "I'm with you!"