You would get the PDFs by querying
mime_type=application/pdf
So, based on your example your full URL would be:
https://www.domain.com/wp-json/wp/v2/media?parent=1267&mime_type=application/pdf
However, it is possible when using the parent=ID parameter, you will see ALL the PDFs, not just the attachments specific to that post. This happens when the PDFs were uploaded to the media library, but not necessarily to a particular page/post.
Perhaps they were linked manually in the page/post, rather than being uploaded and inserted via Add Media or a Gutenberg block. You may also see nothing at all if the post doesn’t have a PDF attached but all the other PDFs in the library have an attachment page assigned.
The query does work as you require when the files are specifically attached to a page/post.
To better explain what I mean, go to your media library and check the “Attachment Details” of one of your PDFs by clicking on it. If it does not include the line “Uploaded to”, then it will show up on all queries to the PDF file type.
However, if it looks like the following, you should get the proper results with the query provided above showing only the PDFs attached to a specific page.
Basically, if the files do not have a specific upload path, the query will show all since it has no way to filter out the stray attachments.