The sale of assigned land by your grandfather was illegal and invalid in the eyes of law because he has violated the conditions of the assignment.
In such cases you can refer to the conditions imposed in the letter granting or allotting him the property.
What was the buyer doing all these 37 years after purchasing the property?
Why he had not taken any steps to get the property mutated on his name after purchasing it by a registered sale deed?
under: "Assigned land" means lands assigned by the Government to landless poor persons under the rules for the time being.
If permanent patta was given to your grandfather towards the assigned land then the assignee/your grandfather can transfer the assigned land at his will.
The Chief Commissioner of Land Administration (CCLA) expressed the view that the lands assigned to the poor and landless prior to 18.6.1954 would not attract the rule prohibiting the transfer of lands. Quoting GO 1142 issued on 18.6.1954, the CCLA opined that there is no prohibition with regard to transfer of lands assigned prior to date of issuance of the GO. Also, there are no prohibitory rules for transfer of lands assigned prior to 1954 in the Prohibition of Transfer of Assigned Lands (POT) Act, 1977.
You may confirm that when it was assigned to your grandfather i.e., whether prior to commencement of the said GO of 1954.
The Section 3 (1) of the Act prohibits transfer of the assigned lands on or before commencement of the Act. It also declares retrospectively that all transfers of such lands which took place prior to the coming into force of the Act will be null and void. “So, the government has to amend the word retrospective to pave the way for regularisation of the assigned lands
The CCLA suggested that the lands assigned after 21.1.1977 can be regularised at market value. However, the assignee should have enjoyed the lands for 30 years.
You may confirm the details on the above lines and proceed with legal process for regularisation.