The special did include a joke Ms. Cummings made about Mr. Trump’s influence on Kennedy Center programming, telling the crowd to “enjoy this fall’s three-month run of ‘White Hamilton.’”

It was not entirely clear why the sex-trafficking joke was not included, or who made the decision.

“While it’s our preference not to cut jokes from anyone’s set, the Kennedy Center has the contractual right to do so,” Netflix said in a statement on Tuesday.

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