How can the legislative branch check the presidents power to appoint a supreme court justice?

Answer 1

The Senate is the only chamber of the Legislative Branch that can check the President's power to appoint federal judges. The President's nomination is completed with the "advice and consent" of the Senate, which can vote to reject the nomination. The President would then have to nominate a new candidate or resubmit the rejected candidate (this has actually worked a few times).

Answer 2

because the legislative branch has more power over the president.

Answer 3

In the United States, the US Supreme Court can determine that a bill passed by the US Congress and signed into law by the President, may be unconstitutional. Thus overturning the law.