The entire text of the main amendment to the Texas Campus Carry bill is available here
. This provision allows for the establishment of gun-free zones on campus as long as two-thirds of the university's Board of Regents agree (click on text to enlarge).
Since the governors appoint the Regents with the approval of the state Senate, I suspect that all or virtually all the Regents are Republicans, and thus it seems likely that it would be very difficult to get 2/3rds of the Regents to agree to sweeping gun-free zones. There is language in the amendment that talks about the university not being able to "generally prohibit" carrying, but that term doesn't seem to be well defined.
Overall, I suspect that the amendment won't greatly weaken the bill.