Marriage with my gradmother's sister's grandaughter

You can marry. Your grandmother and the girl's grandmother are own sisters. Yours will be the fourth generation. So it will not come under sapinda relationship also. As per the special marriage act, A sapinda is someone who has a common ancestor relative within three generations above you on their mother's side of the family or has a common ancestor relative within five generations above you on your father's side of the family. In your case, it is the 4th generation. So there will not be any problem. My son married his grandmother's sister's grandmother only. The marriage is registered and there is no legal problem.
It all depends on you and your family members and the family traditions. In the Telugu States, such marriages are accepted and there will not be any resistance from anyside. So you can talk to your parents and the girl's parents and finalise the issue.

Though the girl with whom you want to make alliance is your distant relative but in no way, it is likely to affect your marriage prospects. However, you must follow the following points prior to finalisation of your marriage-
1) It would be better for both of you to get your blood report after the recommendation of your doctor. If there are no abnormalities seen in the disease like Diabetes, Heart issue, Liver or Kidney disease or confirmation of any disease as suggested by the specialist should be your first priority. In that way, you can ensure your better health regimen after your marriage and even your issues will not contract any severe disease.
2) Ensure that both of you are of the same mental status. Both of you should be reliable to each other. Patience of both of you should also be of highest order. If both of you are not indulged with fighting for the minor issues, there will be the stability of the marriage.
3) Both of you should have decent income so that you can discharge your responsibilities effectively of your issues in relation to their education, health and other expenses. These expenses are apart from maintenance of you couple.
4) Both of you have to devote sufficient time to your issues for their proper psychological growth.

Your relationship with whom you want to get married falls under the spindle. About any person, a spindle relationship will be called a relationship under the spindle to a descendant of up to three generations in the mother's generation and a descendant of up to five generations in the father's line. In this, the generation will be counted upwards about the person concerned and the person concerned will be considered as the first generation, but you will be the fourth generation of the descendant of the mother.

Two persons will be called each other if one person is the ancestor of the other in a row or the two ancestors have the same ancestor in the relationship. We will thus calculate up to three generations in the mother's relationship and up to five generations in the father's relationship to identify the Sapind. Some relationships are prohibited through Sapind but your case is not be considered under this category.

Your relationship does not come in the restricted relationship in the relative relationship of Hindu marriage with the consent and mutual consideration of your family, you can pursue the idea of ??your marriage. As a law, there will be no problem with this. But yes you must get some necessary health check-ups before marriage so that no future child-related problems arise.