Police have arrested a man in his 60s on suspicion of theft following reports of the removal of a loyalist poster in Moygsahel.
He has since been released on bail pending further enquiries.
The banner paying tribute to Wesley Somerville had been erected on a lamppost in Moygashel, but was removed on Friday.
The banner, put up alongside a UVF flag, included an image of two masked gunmen and read: ‘Mid Ulster Brigade UVF, Moygashel. In memory of our fallen volunteers.’
DUP councillor Kim Ashton stressed that she was opposed to all paramilitary groups, but warned that whoever removed the flag risked stirring up trouble.
“There is no doubt that this will stoke tensions in the area and anyone who says otherwise is very naive,” she said.
Referring to IRA murals and graffiti in nearby Dungannon, the councillor claimed the outrage was always one-sided.
“I have never heard nationalist councillors in the area speaking out about images of IRA slogans and guns in the town, which are on display every day of the year.”