The halacha as codified by Shulchan Aruch O.C. 167:6 is that if one interrupts between making Hamotzi and eating the bread, as long as the interruption is related to the meal (not just to eating the bread - see Beis Yosef 167:6 and Magen Avraham) it does not require the person to repeat their blessing.

If one of the people listening to Hamotzi, who has the same rules of interruption according to the Shulchan Aruch, says "thank you" when they are given their slice of bread before they take a bite, does this constitute an unrelated interruption, or can this display of manners be considered related to the meal?

Examples of what is related to the meal, as given by the Beis Yosef, are such things as saying to pass around the food (not just the bread) and telling someone to feed the animals.