There should be no difference in a gallery displayed on a Page or a Post, so your question is quite confusing.
- Just to confirm, are you talking about creating a gallery this way: From the Page OR Post editor, you click on the “Add Media” button above the content edit pane.
- From the popup Insert Media, click “Create Gallery”.
- Select image to add
- Click Insert into page
When I do that, I get a standard [gallery ids="1,2,3"] shortcode inserted into the page or post. When I display the page or post, I get a gallery with the selected images displayed. The image will link to what is called the Attachment page, and the caption is displayed under the image. There are no other links on either a page or a post.
The links and content depend on what is defined with each individual image in the Media Library.
So I don’t know what links you are talking about.