Both players were with the Patriots during training camp but were cut on the final cut day. Now they are back, they have some catching up to do to get ready for the Jets.
"I think the foundations are usually put in during training camp and you kind of go off of that," Koutouvides said. "It's been eight weeks since I've seen this playbook. It's just basically refreshing my mind and getting back to the terminology and the new stuff that was added."
Underwood may be able to help the the Patriots on special teams, especially as a kick returner. He said he began last season returning kicks for the Jaguars, handling most of the duties during the first half of the season.
"It went well," Underwood said. "I feel comfortable back there. Whenever you're an offensive player, you like to get the ball in your hands whether it's special teams or just a play designed for you. It's just another opportunity to get the ball."
Underwood said the new kickoff rules would be an adjustment, but he is open to doing the job if the Patriots ask.
"It's definitely different," Underwood said. "There are a lot more touchbacks this season. The coaches will tell you, 'We want you at this depth, bring it out as long as you don't have to back up' or whatever it may be. It's different for every team. You just listen to the special teams coach and go from there."