I wouldn't rule heavily in either direction.
Instead, I would first give the Black Pudding the Balance check that the Grease spell indicates. If it fails the check, then that portion of the pudding is relatively stable until the rest of the pudding pulls it along. If it makes the check, then that portion of the pudding is half speed until the rest of the pudding pulls it along.
However, the rest of the pudding (5/9ths assuming that a minimum of 5 squares out of 9 of the pudding is always outside the grease) should be able to go around the grease pretty easily.
If this is a horizontal surface, this would barely slow down the pudding since the greased sections should move easily. It gets no traction under the grease to move, but it also gets no resistance. To give the player an idea of what happens here, I would say "The pudding seems to slip somewhat on the grease and then slides across at normal speed and continue on with its movement".
If this is a vertical surface, then 4/9ths of the pudding should have a difficult time and 5/9ths should have a normal time, so basically half speed if the check is failed (5/9ths of the pudding has to move the entire thing) and 3/4ths speed if the check is made (5/9ths + 1/2 4/9ths).
So, horizontally it matters little and vertically, it would just slow up the pudding a little bit.