It is unclear if a Senator or Representative can be impeached.
https://constitution.congress.gov/browse/essay/artII-S4-2/ALDE_00000689/
>Finally, congressional practice indicates that Members of Congress are not officers of the United States. In 1797, the House of Representatives voted to impeach Senator William Blount, the first impeachment in the history of the young Republic. Two years later, the Senate concluded that Senator Blount was not a civil officer subject to impeachment and voted to dismiss the articles because that body lacked jurisdiction over the matter. This determination has been accepted ever since by the House and the Senate, and since then, the House has never again voted to impeach a Member of Congress.
They are subject to recall, i.e. removal by their constituents, and expulsion, i.e. removal by their peers. Impeachment is a process carried out by the legislative branch so how would you form an "impartial" body to adjudicate the charges?
The executive branch could file charges and the judicial branch convict, which historically has led to expulsion, e.g. Jim Trafficant, but I don't think impeachment is an option. If her citizenship were to be revoked she would no longer be eligible to hold the seat.
Trump may be using impeachment in a generic sense.