No, you generally do not grease an automotive starter motor when installing it. Applying grease to the starter's internal components can actually be detrimental. The starter is a precision-engineered device and excess grease can attract dirt and debris, leading to malfunction. The bearings and other moving parts are typically lubricated during manufacturing and shouldn't require additional lubrication during installation.
The only exception might be a very light application of anti-seize compound to the mounting bolts to prevent them from seizing to the engine block over time. But this is not greasing the starter itself.
