The key issue is whether the US divorce would be recognized by Indian courts. Under Indian law, a foreign divorce is valid only if it satisfies certain conditions, primarily that the foreign court had proper jurisdiction, generally where both parties resided or voluntarily submitted to jurisdiction, and that the divorce was granted on grounds recognized under Indian law. It is also important that the proceedings were contested or based on proper consent, and not ex parte without participation of the other spouse.
If your US divorce was by mutual consent, or both parties participated and accepted the jurisdiction, it is generally more likely to be recognized in India.
However, if the divorce was ex parte, or based on grounds not recognized under Indian law, or obtained without proper notice to the other party, then it may be considered invalid in India.
The consequence of this is significant. Even if you remarry in the USA and it is valid there, if the divorce is not recognized in India, you may still be considered legally married in India. This can expose you to allegations of bigamy if you come to India, as well as civil disputes relating to marital status, property, or succession.
Therefore, before remarrying, the safest course is to ensure that the US divorce is legally sustainable in India. This is typically done either by filing a declaratory proceeding in India to recognize the foreign divorce or by obtaining a mutual consent divorce decree in India, if feasible.
In summary, there may not be an issue in the USA, but there can be serious legal consequences in India if the divorce is not recognized. It is advisable to regularize the position in India before proceeding with remarriage.