A competitive scholarship (with a fixed number of awards) would normally lead to students at the margin (with the assistance of their teachers who want them to do well) to work harder and to give greater focus to the test which determines who gets the scholarship.
A performance scholarlship (with a fixed standard for an award) would do the same, but if the standard is based on GPA then it also gives an incentive to helpful teachers to provide some grade inflation. The difficult part is quantifying how much of an impact the different incentives have.
A study of the Georgia HOPE Scholarship after it had been running a few years looked at this. It showed an increasing proportion of Georgia students taking SAT has a B or better, both before and after the introduction of HOPE. This may or may not be grade inflation, but it is difficult to say the scholarships caused it. Meanwhile the average SAT scores of students reporting B or better rose very slightly after the introduction of HOPE; this may be a result of parallel GPA and SAT grade inflation, but again it provides no evidence of grade inflation caused by HOPE scholarships. The report says
At Georgia’s public colleges, this
analysis suggests that at minimum HOPE
has not increased grade inflation
which I think is a fair comment: whether or not there has been continual grade inflation, it has not obviously been accelerated by the scholarships.