Title X of the Act, also known as the Impoundment Control Act of 1974, specifies that the President may request that Congress rescind appropriated funds. If both the Senate and the House of Representatives have not approved a rescission proposal (by passing legislation) within 45 days of continuous session, any funds being withheld must be made available for obligation.
But rescission is for permanently cancelling the spending of allocated or budgeted funds, it is not for just a hold on spending. There is no requirement there for involvement on a hold. There’s whole procedure for rescission, but not for a temporary hold.
On other thing I have noted before is that this particular law, especially where foreign aid is concerned, has never been tested for constitutionality. I think it would fail. It’s not constitutional. This is Congress putting its policy on Foreign Policy when the Constitution very plainly makes the President the controller of foreign policy, not a committee of 535 in Congress.