The Constitution specifies that the justices and other federal judges shall serve “during good behavior.” This is interpreted as a lifetime appointment, subject to impeachment. That’s why this proposal is written as a constitutional amendment. It would need a 2/3 majority in both houses, and then 3/4 of state legislatures would need to ratify.

There’s another idea floating around to impose de facto term limits by regular federal law by rotating justices in and out of lower federal courts at defined intervals.

There are also a bunch of other things that an angry Congress could do to rein in the court (using regular federal law):

• they could use the good behavior clause to impose a written ethics code, or the CLE requirement that another commenter mentioned.
• they can set the court’s jurisdiction (except for suits between states). They can take jurisdiction away.
• On another jurisdictional topic: currently nearly all of the court’s docket is discretionary. They get to decide which cases to take up. Congress can take that power away and force the court to hear appeals on a mandatory basis again.
• Congress controls the annual budget. They get to decide whether the justices have money for clerks, robes, and office supplies or not.
• Congress can specify what dates the court is in session and for how long. At least one time, this power was used to try to prevent the court from meeting.
• Likewise, for a large part of the court’s history, Congress decreed that the court meet in the basement of the Capitol. Not the big fancy marble building. It could happen again.
• as part of its oversight power, Congress has the power to subpoena justices to hearings and to grill them on their decisions on live TV. This actually happened to Justice Kennedy after Bush v. Gore.