Currently there's no way to filter for those cases which are updated by a specific team member.

This information could be partly gathered from the workspace Audit Logs but there are no sufficient filters to narrow down to the specific project and event type.

An attributed 'updatedBy' can be introduced to give info on the last user to have made an update to the case. Queries could also make use of this attribute.

Use-case:

So I made a task for a QA engineer to update a test suite in Qase.

And I want to see what is updated, so I can make a review on it.

I don't want to use review feature for this but a simple query/filter to see, which test case is updated would be quick to find out.

In JQL it is implemented as 'last updated'. If you check jira, you can filter for updated, 'last updated <1d' or similar things.