It was on rubber grommets to reduce vibrations, and Mission Control asked Fincke to remove them and just bolt the piece down.
"We're very hopeful for this, and if not, we have a few other tricks up our sleeves," Fincke said from the space station after the task was finished.
The astronauts have been trying to get the system running for four days, but the urine processor has worked for just two hours at a time before shutting down. A normal run is about four hours.
An initial test after the repairs ran for almost three hours before shutting down Sunday night. Engineers again were trying to figure out a fix.
As a last resort, Endeavour could bring the problematic part back to Earth for repairs when the shuttle departs on Thanksgiving.
That option could complicate plans to add crew members to the station since several water samples need to brought back for tests before astronauts can drink from the contraption.
Samples will be brought back on Endeavour and in February on space shuttle Discovery.
The water recovery system, delivered a week ago by Endeavour, is essential for allowing six astronauts to live on the space station by the middle of next year.
"Without being able to recycle urine, that does take down some of our capability," Fincke said. "It's not necessarily a show-stopper but it's something that we definitely need to address."
Engineers were studying whether six people could still live at the station with the urine processor working two hours at a time, said flight director Courtenay McMillan.
"We don't know if it's a good idea to start and stop it multiple times," McMillan said. "We may be breaking something further until we really understand what's going on."
Flight controllers had hoped the water samples would have a mixture of 70 percent from condensation and 30 percent from urine.
Given the problems with the processor, that ratio stands at 90 percent condensation and 10 percent urine.
Mission managers have decided not to extend Endeavour's trip by an extra day since the astronauts have enough water samples.
While Fincke worked on the processor, Endeavour's seven astronauts had part of the day off Sunday, except Pettit who gave up some of his off-duty time to work on the water recycler.
Astronauts Stephen Bowen and Robert "Shane" Kimbrough prepared for the fourth and final spacewalk of the two-week mission. The spacewalkers will finish cleaning and lubing a jammed joint, which allows the station's solar wing to rotate in the direction of the sun. They also will lubricate a twin solar-wing joint, which is running without any problems.