No. of Recommendations: 1
Judgment in Cases of Impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust, or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment, and Punishment, according to Law.
Thus, the Constitution is clear the purpose of IMPEACHMENT is not to exact legal punishment but to remove an elected official from office. It thus also means that a decision by the Senate to NOT remove an elected official also has no bearing on that official's fate in front of a criminal or civil proceeding.
I haven't read the motion, but the plain text of the Clause gives them at least a way out of that. It only says that a Party convicted can be subsequently indicted. It doesn't say what happens when a Party is acquitted.
I imagine that they're arguing that if the Senate convicts, then the accused can then be subject to further criminal proceedings - but that if the person is acquitted, then that acquittal works to block a subsequent criminal case.
I don't think that will be persuasive, but it should be enough to avoid being sanctioned for a frivolous argument.