You don't stop it. If you link in from an outside site like photobucket, then the picture is a link to that site.
In photobucket, you can however make albums private. So for instance half my albums are public, half are private. When you link in, you can see only the ones I deem public.
I've also gotten a little careful with the naming of my albums. For a while I used the stream name. And then I'd post pics of fish without saying the location, but low and behold, if you clicked on the pic it took you to an album named _____ Creek, lol. Now I just use dates.
The other option is to just attach the picture. Do the full "reply" by hitting the blue button, instead of the quick reply at the bottom. Then at the bottom you can browse for a file and attach it. If it's a photo, it shows up just fine. The problem with this approach is that the file size has to be under 1000k, and in jpg format. You can switch formats with MSPaint, just open it in paint and save it as a jpg. Check file size. And many of the photo programs allow you to resize pics, even the cheap windows based ones. You don't need photoshop or anything that fancy just to do that.
Edit: The attach feature allows gif format as well, but they are generally much larger than a jpg.