Refresh secrets from Secret Manager in ECS tasks

We have running ECS-tasks and for accessing other systems we have saved credentials in our Secrets Manager. In Secrets Manager we have to change the credentials and we are going to do that manually in the AWS console. We figured out, that this information is cached in the ECS-tasks. How can we invalidate the cache? We found out, that just restarting the ECS-tasks didn't help, but we had to force a new version of the task definition. Is there a different way of doing that without creating new tasks?