How to get docker in docker logs in K8s cluster?

I have Promtail installed as a daemon set on my cluster (as part of stack).
In the cluster, we run Gitlab runner which sometimes has docker-in-docker (DIND) jobs, which means that inside the build container in the pod, we have a command of docker compose up -d to test some components.
For these components we need logs, but the logs are inside the docker of the pod.
What can be the right way to extract them or get them so Promtail can push them into Loki?
And how I can make sure they will be attached to the pod?