He was just trying to show the Arbiter how the Covenant and the Forerunners (by way of a Monitor) talk about the same thing but have vastly different understandings.

I thought it neat that when the Gravemind says "this one's 'containment'...", referring to 2401 PT, he growls a bitter growl. Nice touch.

What both the Monitor and Regret were saying were in keeping with both of their characters. Why would you think their dialogue was staged by the Gravemind? I see no indication of that at all. The Arbiter didn't seem to think much of the exchange, at which time the Gravemind says, "If you will not hear the truth, then I will show it to you." He then teleports the Arbiter to within sight of the Halo control room to witness what's really transpiring. It's all confirmed when he asks Guilty Spark about Halo to then try and convince Tartarus to stop.