As shipped with ICD 7.6 (at least on Linux x86 64-bit), ITIC isn't quite configured correctly. When you try to run startFusion.sh, it will complain that it cannot file the main class. The problem lies in the init.sh script. Specifically, you need to change the following line:
Without this change, it's trying to find a file named IntegrationComposer7510.jar, which doesn't exist. In 7.6, the correct file is IntegrationComposer7600.jar.
Another thing to note is the URL of the BigFix server for use with the ITIC mapping is: