The short answer is that we have no evidence to suggest that this was a consideration by Roman rulers post-conversion. With the caveat that absence of evidence is not evidence of absence, so to speak, I would suggest that it is highly unlikely we will find any.

The major reason for my suggestion is that the idea that a state should apologize for an action taken by previous incarnations of the state or previous rulers of the state is a relatively new one, rooted in postcolonialism. To expect that a Roman ruler would offer an apology or feel guilt for what was, at the time, a completely legal action taken by a provincial governor is to hold that ruler to improbably anachronistic standards. The Roman state, as we define it, emerged and collapsed 1400 years before the concept of state succession. The concept itself is built on a few hundred years of post-Westphalian political theory. To expect a Roman ruler, or Roman Christians, to feel any sense of responsibility, let alone guilt, for an action that contributed to their own religious lore is nonsensical.