First identify your image.

$ docker ps --format "{{.ID}}: {{.Image}} {{.Names}}"
3d2fb2ab2ca5: jenkins-docker jenkins-docker_1

Then login into the image as root.

$ docker container exec -u 0 -it jenkins-docker_1 /bin/bash

Run command in stopped container

$ docker run -u 0 -it jenkins/jenkins:lts-jdk17 bash

Now you are inside the container, download the jenkins.war file from the official site like.

# wget wget http://updates.jenkins-ci.org/download/war/2.176.1/jenkins.war

Replace the version with the one that fits to you.

The next step is to move that file and replace the oldest one.

# mv ./jenkins.war /usr/share/jenkins/

Then change permissions.

# chown jenkins:jenkins /usr/share/jenkins/jenkins.war

The last step is to logout from the container and restart it.

$ docker restart jenkins-docker_1

You can verify that update was successful by access to you Jenkins url.