The second Mishna discusses and then concludes that other types of Temple services cannot be performed outside of the Beit haMikdash. If a ka-zayit from one of the meal-offerings was sacrificed outside of the Temple courtyard, those performing the service would be liable. However, Rabbi Eliezer rules that a ka-zayit would not be enough to disqualify the entire meal offering. It would take the entire meal offering to be offered outside for that service to be significant.
Rashi explains this by suggesting that Rabbi Eliezer believes that an olive-bulk would be enough to hold people liable in the case of an animal sacrifice done outside of the Temple courtyard. This is because a typical animal sacrifice is valid even if some of the meat is missing - thus performing that service outside of the Temple is forbidden.
Meal-offerings, however, must be brought as a whole to be valid. Bringing a partial meal-offering beyond the Temple courtyard is not meaningful. On the other hand, a meal offering brought in the Temple with a ka-zayit left over and brought outside the Temple would be punishable. In this case, the meal-offering was brought in a forbidden manner.
It strikes me that we have been learning the different ways that one could invalidate an offering/be held liable in different categories: time, place, person, order, and more. And today we have learned about amounts of different offerings in different places. There seem to be a huge number of ways that one could violate the rules of offerings. Perhaps that is part of the reasoning behind our extremely ritualized prayer services. Our prayer services stand in for our inability to offer sacrifices.