The prompt that tells you to 'enter a service item for this customer' when you create new Task with time entry on regular CRM Task record (or from a Project) shows up only if the entered time is marked as Billable. Service Item is a requirement to Save a new time that needs to be billed. To be able to save the Time Entry if the time spent will not be billed, unmark Billable column on the New Time Tracking sub tab on Task record.
Steps to reproduce error:
Create a Task with Time Entry
1. Navigate to Activities > Scheduling > Task > New
2. Enter Task details
3. Click Time Tracking tab > enter Duration
4. Click Add
Actual Result: "You must enter a service item for this customer".
1. Navigate to List > Relationships > Project > Open the project record
2. Click General tab> Activities Subtab >New Task