Short version:
– Open Messages on your iPhone or iPad, scroll to a picture/video you want to delete.
– Touch the picture/video (don’t press, just lightly touch) until a menu appears.
– Select More… from the menu
– Be sure your image has a check box to the left of it.
– Tap the trash can icon in the lower left to delete the image.
If you have some videos in your Messages timeline, this is a nice way to free up space. Remember, these deletes are permanent, so back up your phone before you go on a deleting rampage.
UPDATE: Even better way (H/T Mike Goril), open Messages, tap Details button in upper right corner, scroll down to ATTACHMENTS area, touch and hold individual images, tap Delete from the menu that appears.
Even better, better way: Open Messages, tap Details, scroll down to ATTACHMENTS area, touch and hold one image, tap More from the menu that appears. Select multiple images, then tap the Trash can in the lower right.
Bingo. I was literally just typing the same thing. This is by far the most efficient way.
A faster selection in the detail would be nice. Like photos.app tap and drag to select multiple.