I actually did some checking along those lines before I got your message.  I used a notification instead of a display alert, but the result is that the "TeXShop" block of code is definitely not being executed.  Never the less, deleting the tell block from that code will still stop TeXShop from opening.  I noticed you had to delete the tell block and not just the code within the tell block.  Some online searching led me to the following which seems likely to be the root of the problem:

http://stackoverflow.com/questions/12431811/how-to-make-applescript-not-automatically-open-applications-in-tell-blocks