Here's my hunch: The NFL grievance is about trying to delay the NFL players' right, without decertifying prior to the expiration of the CBA, to bring an antitrust challenge against certain NFL practices. This is based my reading of a particular provision buried on p. 238 of the NFL Collective Bargaining Agreement: Article LVII(3)(A).
Upon careful review, Article LVII, Section 3(A) of the NFL collective bargaining agreement (p. 238 of PDF) states as follows:
Following the expiration of the express term of this Agreement ... if the NFLPA is in existence as a union, the Parties agree that none of the Class Members ... nor any player represented by the NFLPA shall be able to commence an action, or assert a claim, under the antitrust laws for conduct occurring, until either: (i) the Management Council and the NFLPA have bargained to impasse; or (ii) six (6) months after such expiration, whichever is later.Thus, pursuant to Article LVII, Section 3(A), the event of impasse would trigger the start to a six month waiting period before the NFLPA, if it is in existence, could attempt to challenge the NFL salary cap, draft and other labor-side restraints under Section 1 of the Sherman Act.
As a matter of law, however, impasse cannot occur where the party seeking to benefit from declaring impasse has bargained in bad faith. Therefore, if the NFL can show that the union is engaged in some sort of "bad faith" bargaining, impasse would be delayed, and so too would be the players rights under the collective bargaining agreement to bring an antitrust suit against the league's draft, salary cap and other restraints.
Of course, the thought of the NFLPA bringing an antitrust challenge against certain league-wide practices is a real fear for NFL team owners. Indeed, the NFL players, after a failed strike, implemented this strategy successfully in the case McNeil v. Nat'l Football League, 790 F.Supp. 871 (D. Minn. 1992).