The easiest way to turn off link sharing is through the Samsung Messages app.

Link sharing is part of Samsung Social, a feature that lets Galaxy smartphone users share photos and more. It lets you share 5MB and larger files to other Samsung Galaxy smartphones using a link instead of the actual file. This feature can be convenient if you or the recipient has an older phone or limited data. If you use link sharing when sending images or other files to a non-Galaxy smartphone, it will send it as an attachment. Samsung Social also helps you quickly find other Galaxy users. Link Sharing is also an app, so you can also go to Settings > Apps > Link Sharing > Disable to turn it off. You can also edit other settings for the app too including using it over Wi-Fi, auto-deleting expired files, and more.