Dear Ms. Mcguire,
Thank you for posting on History Hub!
Using the information provided in your post, it is unclear who 'S. Tablock' was married to. If your grandmother said that "someone" on your grandfather's side of the family married a Native American, that could be anyone, not necessarily a direct ancestor.
We suggest you start with piecing together your family tree with the information that you do have beginning with yourself and your parents. Census records are a good place to start. You may wish to search Ancestry or FamilySearch for the U.S. Census. There may be a fee for using Ancestry. Instead, please check for access at your local library as many library systems subscribe to these sites, making them free for their patrons.
Ultimately, use the information you have and see where the records take you. The Department of the Interior has a website on tracing your Indian Ancestry. To keep your research organized, we suggest you input your information onto a family tree using Ancestry (fee-based) or FamilySearch (free).
We hope this information proves useful to your research!