I booked a ticket via TY site with points + cash 5 weeks ago. The T&C specifically say that points are non-refundable in the event of cancellation AND there is a TY fee for any changes to the original ticket in addition to any fare differences and change fees from the airline.
I had been doing dummy bookings for 1 month prior to finally booking. The T&C have been consistent as above during that time (about 2.5 months before this weekend). I never saw any wording about TY points being refunded.
TY does NOT have a refundable 24 hr grace period after booking and also states no refund of the points used (price of the old ticket will be applied to a future ticket less all airline fees).
Since you cancelled via United last time, can you do the same this time?