Who can delete from the Bitbucket Push Logs

[Terraster]

The Push logs (https://confluence.atlassian.com/bitbucketserver/push-logs-998882984.html)
are also kept for deleted branches.

Who can delete this log entries?

It looks like they stay forever, our bitbucket admins could not help us in this question.

[v8lust]

I believe this report is based on the Git commit history itself and not a separate log in BitBucket. Assuming this is true, you can use BFG Repo-Cleaner open source tool. This is a JAR file which can hard delete from Git.

Note: this is commonly used to removed Binaries or sensitive data that has been accidentally committed to Git.

[Terraster]

In a test repositry I have used git reset HEAD~n to squash to the repo to a single commit and push with force. 
After a test checkout the local history has exactly one commit and also the Bitbucket repository has exactly one commit

With the exception of the push logs (https://confluence.atlassian.com/bitbucketserver/push-logs-998882984.html)
here you can see the force push and and also still the old old commits, you can easily reproduce with the method described above.

Again to clarify I'm talking about the push log (found under the repository settings)
and not about the also available commit history of the repository.