Grinstead, a 30-year-old high school history teacher, was reported missing when she didn't show up for work Oct. 24.
So far, police are calling this a missing person case but they haven't ruled out foul play.
Searches have been conducted every day in various ways, including on foot, by horse, with helicopters and with all-terrain vehicles. Wednesday, cadaver dogs were used, though authorities stressed it wasn't because they were looking for a body.
An $80,000 reward is being offered for information leading to the safe return of the former "Miss Tifton" and contestant in the Miss Georgia pageant.
Anita Gattis, Grinstead's sister, says police "didn't find a lot" when they searched Grinstead's home in Ocilla, Ga.
"The house was locked," Gattis told The Early Show co-anchor Hannah Storm Friday. "Her cell phone was back in the charger. She always takes her cell phone with her everywhere she goes. Her purse and her keys were missing. The car was home but it was unlocked, which is very unusual. Tara always kept her car locked."
Gattis says she suspects her sister left the house under her own will "and then something went very wrong after that. I don't know if it started out to be an abduction and she was just lured out of her home, or she went with somebody and then something happened. I'm just not sure. But I really do feel like it is an abduction at this point."
Authorities have questioned a former boyfriend of Grinstead's, Gattis confirmed. "They broke up about nine months ago," she says. "He has been questioned many times at length. He has obtained an attorney.
"They had had a very bad argument, I just found out, several days before she went missing, concerning an 18-year-old that he was dating. My sister did not think that (the 18-year-old's) parents would approve of a 30-year-old dating an 18-year-old. I'm told that she threatened to tell the parents, and they had a very heated argument over this."
A former student accused of stalking Grinstead has also been interrogated.
Gattis says he was arrested several months ago, adding, "She had taught him when he was in the ninth grade. He had just recently graduated. I think, maybe, after (Grinstead) and the boyfriend broke up, he kind of saw a window of opportunity, although Tara would never, ever date a former student. He was arrested attempting to break in her house, and she was at home at the time."
Grinstead was much loved, and highly respected in the community, Gattis says.
"Tara is a wonderful person," she says. "She's a wonderful, Christian person. … She was very active in the 'Relay for Life' cancer program (in Ocilla). She started several beauty pageants (in Ocilla). The students loved her. They thought of her as more of a friend than a teacher."
If you have any possible information about Grinstead's whereabouts, police ask that you call 912-386-2564. You can also go to FindTara.com.