I agree with both the post above, Normally you would be able to hide the screen fields using the table V_T588M, and I believe you have already tried route of V_T588M (looking at your screen shot), I would suggest you to try using the method suggested by Glen. If this doesn't work then you would still will be able to hide Screen Dialog box using the method I have originally suggested.
To my understanding Technical fields are grouped together in various screen filed group and some times these groups override the screen control set by V_T588M (this could be cross checked by looking at the same table , even if you make some fileds mandatory they might not appear on your screen)
now if you don't have ABAP resource, you could have a go at it if you manage your self an object key. If you do go down this route and need help shout...
Once you have modified the screen dont forget to activate the screen otherwise your changes would not work. Have fun
Best luck.