You have to understand what a swarm is.
It is a group of tightly packed creatures. So tightly packed that affecting some of them at one edge (in this case bottom) of the group does nothing to the group as a whole.
300 non-flying tiny creatures (cat sized) or 1500 non-flying diminutive creatures (bat sized) or 10000 non-flying fine creatures (insect sized).
1000 flying tiny creatures or 5000 flying diminutive creatures or 10000 flying fine creatures.
Swarms are never staggered. They cannot be tripped, grappled, or bullrushed.
They cannot be knocked prone. Hence, they cannot fall down.
Although a small portion of a non-flying swarm at the bottom will be in the Grease, that is basically irrelevant to the majority of the swarm.
No effect.