How can I delete all message attachments?
Source.  This can be done with both Attachments and Images:


Launch the Messages app and open a conversation that has attachments you want to get rid of.
Tap on the blue “i” button at the top right of the app.





In the new interface that appears, scroll down and then tap and hold on one of the attachments in the grid view to reveal an Action Menu.
Tap on the More… button to select the attachment you were just tapping and holding on.





A blue check mark will appear, and so will several empty circles on the rest of the attachments; tap on each of the attachments you wish to delete to select them and this will put a blue check mark on those attachments as well.
Once all of the attachments you want to delete have been selected, tap on the blue trash can icon at the bottom right of the app.
In the pop-up menu that appears, tap on the red Delete … Attachments button to confirm deletion of your selected attachments from your conversation.
All those attachments will now be removed from the conversation, but your conversation itself will remain; double-check the conversation to verify.