For example we have cluster in AWS ECS with 3 services:

And we want to change evn variables in api-staging service.

To do it we should create a new revision of task definition with updated env variables and then tell the service to use new task definition.

So, to create a new revision of task definition we should go to list of all revisions, select the last one and create a new revision.

To change the container evn variables we should go to container definitions section and edit our container:
Set new values to env variables and then update container and save new revision of Task Definition:

When we have a new revision we should update our api-staging service and set the latest revision. Also don't forget to set force new deployment checkbox