Frese's new contract includes a base salary of $1.4 million.
Owusu was held scoreless in the fourth quarter in the Terps' season-ending loss to Texas.
Maryland is looking for its first Elite Eight appearance since 2015.
Reese scored 19 points, grabbed five rebounds and dished out a pair of assists against Alabama.
Brenda Frese's squad tallied 22 assists on 42 made shots.
An Alabama beat writer breaks down the Crimson Tide before their second round matchup with Maryland women’s basketball
Alabama has struggled to end the season, losing seven of its final 11 games.
The Terps are looking to make the Sweet Sixteen for the first time since 2017.
The Terps held the Mountaineers to four points on 12.5 percent shooting in the second quarter.
Star sophomores Ashley Owusu and Diamond Miller took over as the Terps advanced to the round of 32.