Looking on the community-contributed section of the iApp code share, I found the Websense CG template page, and there is a more recent version, although the author did not post any notes about it fixing your particular issue. If you want to install this, the steps would be: 1. download it; 2. import the new template; 3. re-parent your running iapp to this new template and click "Finished". If the new template does not work for you, simply re-parent back to the one you are using today.
You asked about strictness. Strictness protects the configuration related to your application from being altered from outside the iApp (by using the regular UI or tmsh, for example). You can leave strictness on while re-parenting (upgrading) your iapp, and it should work just fine. If you turn strictness off and begin changing settings outside the iApp, you will have disengaged the sync between the iApp's data and the real system config. If you re-run the iApp at that point, the changes you made outside the iApp may be overwritten. You can avoid making that mistake by re-parenting the iApp to "None - Do not use a template."