What is a claim for benefits? If HCE complains that he was cut back in ADP testing, is this a claim? What are consequences if we do not follow plan procedures in answer?

A claim is a request for a plan benefit by a beneficiary. (29CFR 2560.503-1(d). A benefit under a 401(k) plan is the right to make tax-deferred contributions. So you've got a claim.

Processing a grievance under a plan's claims procedures tends to insulate you against a lawsuit. So you probably do want to follow those procedures, if the participant won't take your oral explanation as an answer.

Failure to follow the claims & review procedure may result in de novo rather than discretionary review by the court.