Never into a sewage line going to a septic tank or other on-site sewage disposal system.
Almost all cities prohibit running gutter water or ground water or rain water into the sanitary sewer. Some cities let you drain to a storm sewer which is a separate system from the sanitary sewer.
Acceptable places to drain underground gutter collector piping:
1. Into a pit where a sump pump sends it away from the house,
2. Into a dedicated leach field (which can be constructed in the same manner as a French drain, in the same manner as a septic tank leach field, or any method in between),
3. Terrain permitting, a down sloping undrground pipe that eventually reaches the surface.
The good conscientious technician or serviceperson will carry extra oils and lubricants in case the new pump did not come with oil or the oil was accidentally spilled, so the service call can be completed without an extra visit.