For those wondering what the injury settlement time period is, it's determined by the player and the team as part of the settlement process:
Injury settlements
The next phase for a player who is not claimed after being Waived/Injured, they have five days to reach an injury settlement with the team. Injury settlement keeps the player from going on IR for the rest of the season. If a player and the team come to an injury settlement, a player is released and compensated for the amount of time agreed upon by both parties in which the injury would keep the player from being able to perform their NFL duties. The player is then free to sign with any team at that point but may not sign back with the original team until the length of the injury settlement has concluded as well as an additional three weeks.
The typical structure of an injury settlement would be to pay the player the portion of their base salary they would be paid weekly times the number of weeks agreed upon for the injury. For example, if the two parties decide the injury would take six weeks to recover, a player would be paid 6/18ths of their base salary.
If the two parties do not agree on an injury settlement, then the player goes on IR for the remainder of the season. In either case, the amount of salary paid to the player either from an injury settlement or from being on IR counts against the team’s salary cap for that season.
Source,
a useful Steelers fan page.
So presumably, prior to week 1, the Pats settled with McDermott for a 3 week injury settlement, paying him 3/18 of his salary ($300K,
based on SpotTrac's citation of a $1.8M base salary for this season) rather than outright releasing him. They likely then shook hands and said, "Please don't sign with anyone else, and we'll bring you back to the PS in 6 weeks minimum." He signed back for the league minimum (just under $290K).
That said, even prior to his injury, he looked pretty bad in preseason, though nowhere near as bad as Lowe has looked in season, so hopefully, he can be added back to the main roster, though at whose expense (Reiff? JJSS?), we'll see.