You have a storage bucket that contains two objects.

Ensure that the object you don’t want to be cached anymore is not shared publicly.

Create a new storage bucket, and move the object you don’t want to be checked anymore inside it. Then edit the bucket setting and enable the private attribute.

Add an appropriate lifecycle rule on the storage bucket containing the two objects.

Add a Cache-Control entry with value private to the metadata of the object you don’t want to be cached anymore. Invalidate all the previously cached copies.