This is not an uncommon challenge.
Here were my thoughts.
1. I am thrilled to know that the grades matter to the students and their parents. They likely have a strong association betweeen learning and grades. View this emphasis on grades as an emphasis on learning.
2. If you want to give re-takes primarily to give more points, you are missing the point and have forgotten the purpose. Testing is an opportunity for students to demonstrate their understanding. Re-takes should be for the same reason.
3. Choose your own adventure. Do you, as the teacher, want to engage in conversations about points or about learning? If you make the test about points, you are choosing the points adventure. If you make tests about learning, you are choosing the learning adventure.
4. If the results are not as good as you anticipated (based on class observations, pre-test reviews, student engagement, etc.), have you considered why? It may not be because they "didn't study enough."
5. As the teacher, what did the test (or re-take) teach you?