ABC News has not verified the letter with the committee, which has declined comment.
"It is perfectly normal that the committees would want to make sure that they received all pertinent records. We did review this account at the time and there were no responsive or relevant documents there," Kushner's attorney, Abbe Lowell, told ABC News.
"The committee was so informed when documents were produced and there is no issue here," he said.
The revelation that Kushner and at least five other senior White House aides have used private email accounts to discuss official business is being taken seriously by Republican-led committees in Congress.
The House Oversight Committee has also opened an investigation into the use of private email and encrypted communications programs by White House and administration officials.