Not much, but you can untick the jusched.exe from Msconfig. It is only an update facility. It may be a personal issue, but I have mine scheduled monthly in the Java panel and also do manual checks, whenever I rememember.
However, that would not solve your problem. I have absolutely no Knowledge of Matlab, but browsing I can see it is a language of its own. Maybe, therefore, it conflicts in some way. You could try turning off the debugging in Java in the Control Panel - Java - Advanced tab.
You can also scroll down, while in there, and look at the "Micellaneous" section and see if the icon is turned on. If it is, the next place to look is down on the taskbar. Click the small double arrow over on the right "show hidden icons" , and then "customise". Check that the Java item is set to show icon and notification activity.
But, during my browsing, I noticed this. Maybe it is a path to your problem:
MATLAB Builder JA (for Java language) - MATLAB
fwiw.
I have always uninstalled Java, or other programs, through the window facility Now called Programs and features. To date it has never caused any conflictions.