OK Karen.
Looks like you are only using the diffuser, not as a diffuser, but just to hold your fibre-optic cable so that it can 'sense' the internal flash.
For such an arrangement it would be preferable not to have ANY light from the built-in flash emerge from the front of the diffuser (or escaping from around the clear plastic of the rest of the housing). Any such light may contribute to backscatter from particles in water.
I used to use a small Sea & Sea YS25 strobe and held the fibre-optic cable in place by drilling a hole through the diffuser and packing the inside of the diffuser with aluminum foil. Like for your setup, it was just another way of using the diffuser to hold the cable where it can 'sense' the internal flash.
Here are some photos of how I set it up:
So for your setup, if you can relocate your fibre-optic cable somewhere else, then just a small shaped cut of the diffuser should allow you to get back where you were before you got the Inon mount!
As Interceptor121 has indicated, Inon actually has another solution called their 'Clear Photo System':
INON Technical Guide [Clear Photo System]
For this, you stick a unique dark filter over the TZ5 flash before putting the camera in the housing. This blocks out visible light from the flash, but allows a non-visible light signal to get through to the fibre-optic cable of the strobe. The fibre optic cable is mounted in front of the built in flash, on the bracket on the housing that is revealed when you take off the diffuser.
Here is a photo of me testing it out by taking a photo into a mirror to check that there is no light leakage from around the built-in flash (circled in red). You will see from the Inon write-up that other people cover their clear housing with black masking tape to reduce backscatter!
Hope that helps!