Earhart was trying to become the first woman aviator to circle the globe when she and her navigator, Fred Noonan, disappeared in the South Pacific in 1937.
TIGHAR has staged repeated expeditions to search the waters around the Kiribati atoll of Nikumaroro, about 1,800 miles south of Hawaii.
Gillespie said Thursday that the group is raising money for another expedition planned for this fall that would use two submarines from the University of Hawaii to search the reef they believe holds the plane's wreckage.
Gillespie's group is concentrating its search on a reef abutting the atoll, then known as Gardner Island. They say the plane might have been washed off the reef by high tides shortly after the landing and that the wreckage may be found in the deep waters nearby.
The group is concentrating now on analyzing a piece of aircraft aluminum, about the size of a dinner tray, discovered on the island in the 1990s, Gillespie said. While the rivet pattern on the piece didn't match the Lockheed Electra, he said they're now focusing on whether it could be conclusively identified as a patch that was placed on Earhart's plane before it disappeared.
"It's always so ironic to be working on this stuff, and then at the same time fighting a lawsuit that says, 'Ah, you found the thing years ago,' " Gillespie said.
The U.S. State Department in 2012 lent its expertise to the search, analyzing a 1937 photo of the shoreline that shows a blurry object sticking out of the water that some experts say is consistent with the strut and wheel of a Lockheed Electra's landing gear.
Expert witnesses for Mellon filed statements in court earlier this year in which they superimposed drawings of objects such as the landing gear of a Lockheed Electra over shapes on video from TIGHAR's exploration of the sea floor in the area.
"The objects we have identified in the 2010 video footage are consistent with parts of the Earhart Lockheed Electra Model 10 and, in the absence of an alternative explanation for the source of those objects, we conclude that they are likely to have originated from Earhart's Electra," wrote Rhode Island engineer John D. Jarrell, one of the experts who reviewed the video for Mellon.
In opposing TIGHAR's request to dismiss the lawsuit, lawyers for Mellon argue that factors influencing the group's decision to keep the discovery secret included the lack of any agreement with the government of Kiribati about rights to the wreckage and an exclusive publicity agreement with Discovery Communications, which was filming the expedition.
Tim Stubson, a Casper lawyer representing Mellon, said Thursday, "We wouldn't have brought this action and pursued it as far as we have unless we were sure that the plane is there and the plane has been identified and TIGHAR knew the plane was there."
Gillespie said that if TIGHAR ever is successful in finding Earhart's airplane, there won't be any doubt what it is.
"If we end up with video of that moment, when the wreckage of the Earhart aircraft comes into view, and if it does, it will be clearly that," Gillespie said. "It won't be something like Mellon talks about with some vague shape of encrusted coral. If that airplane's down there, it's going to be obvious to anybody. It's just a matter of hitting the right spot, and we haven't yet."