This is a migration from https://otrs-wiki.wikimedia.org/wiki/OTRS_technical_challenges.
Attached images are sent with a content-disposition header so that they cannot be viewed in the browser, only downloaded. It is a slight inconvenience only, but also an easy fix, I presume.
Looking around, this could be because http://www.otrs.com/open-source/community-news/security-advisories/security-advisory-2005-01/ of the security vulnerability way back in 2005. However, as we are on a more recent version, this shouldn't be problem.
I believe the configuration needs to be changed from:
AttachmentDownloadType is set to "attachment". to (AttachmentDownloadType = "inline") (the default configuration).
This could be something in the admin interface?