...
When viewing the client's transactions, click on the Entire Service History tab.
This will show you all service transactions. Each will have a Need (this was created automatically when you created the Service) and a Service. Click the trash can next to the Need to delete both the need and the service at the same time.
If you click the trash can icon next to the service first, the need will remain in the system
This deletes the transaction for the client whose profile you are on. You will need to repeat this process for every additional household member listed on the transaction.