Remove link function from oembed image or video

WordPress has very limited control over the embedded content. When you put URL to YouTube video (for instance), WordPress calls the oEmbed URL for that service (YouTube in this case), and YouTube returns the complete HTML for embedding the content. That can be a different thing, including IFRAME, and each service has own oEmbed content format.

If you want to make changes, you need to modify that HTML sent by the service, and modifying it can break it.

As far as I know, there are no plugins that can do that, and the only way is to make your own HTML parser for the service you want to use, process HTML returned, and modify it before saving.