Hindu law for marriage among close relation.

Your father's mother's stepmother's son's granddaughter. She may be your cousin. The relation will be under Sapinda relation as yours is the 4th generation from common blood relation. Such marriages are not as per the law except in case such marriages are in practice in your area and community.
You can marry her, There will not be any problem if there are no complaints from either side. So your parents and the girl's parents should sit and discuss and they have to accept the proposal. In such a case, you will not have any problem. But if they don't agree and if they complain the marriage will become illegal.
So the first thing you should do is to convince your parents and she has to convince her parents. Once they give their acceptance you can go ahead without any hesitation.

As indicated by you both of you would be cousins and as such such a marriage is prohibited under the Hindu Marriage act as such relationships falls into Sapinda Relationship.
However, you have to see the custom of your society and if such marriages have taken place in your society and the couples are enjoying blissful lives after their marriage knots, you can think of such a marriage. However, you need to take your parents into confidence and in turn your parents should proceed for talks with the family of your fiancé. This should proceed with the cordiality and the relationship is settled amicably.
In that way, your relationship would be smooth in your marriage journey but keeping in mind of such a closed relationship, take the suggestion of your physician who might evaluate DNA and other blood tests to ensure that no complication would arise as a result of such an alliance.

As mentioned above both of you are cousin. As per hindu law such marriage is not allowed as your relationship comes under sapinda relation. Many people not accept this marriage because born baby from this relationship are found biologically unfit. But nowadays such marriage is being done. In your community if such marriage is allowed then you can go ahead. You should talk with girl's parents regarding marriage. If they are agree you shuld also accept their proposal. Legally there would not be any problem.

As per the Hindu Marriage Act 1955, the marriage made within Sapinda relationship is considered illegal. Sapinda relationship is traced upward counting the party (person involved) as first generation and then it extends up to 3rd generation in the line of ascent through the mother and up to 5th generation in the line of ascent through the father. Sapinda relationship was considered basically to avoid marriages between the near cousins as per the Hindu tradition and culture and same was then incorporated under the Hindu Marriage Act.
You are falling under the same relationship and legally you cannot go for this relationship. Now there are some exceptions in this matter that if this is considered normal in a community due to the local customs and is a fact of matter then one can go ahead for that kind of relationship. So, you have to consider these points before going ahead in the matter.
Another important thing in this context is that sometimes there may be separation between the couple due to differences and if the marriage is not under the legal framework then the contesting lawyers can take advantage of this fact to the advantage or disadvantage of one of the partners. In other words the legal fight would become more complex.
You can take a proper decision in the matter considering all the above aspects.

Marriage with close relation is not a mistake as per the stipulations laid down in any religion, But the marriage within tge gothra is objectionable as the same gothra boys and girls are considered as brothers and sisters. There may be questions whether the marriages against the rule are not good. To answer this it is not correct to marry against the rules laid by the religions and violations or violators should face the consequences if any happened later. Many arranged marriages itself facing problem in later stage. The major thing in a married life the mutual understanding should be there between the couples and on no situation they should think or discuss that this marriage found mistaken one as it leads to separation or chaos.