360 la weighted flex plate do I need to rebalance?

This is their screwup and not yours. If they won't pick up the tab for their mistake, I'd dispute the charge with your credit card company- you did not receive what you ordered.
When they balanced my first engine build in my dart it was an external balanced he used the stock harmonic balancer, one with counter weight and a B+M counter weighted flex plate as the B and M torque converter was not counter weighted. Engine ran very smooth. Second build used a scat forged steel assembly internal balance bought harmonic balancer from scat had machine shop cut counter weight off flex plate in lathe and neutral balance it. Assembled it and it run real smooth. The difference in bob weight from stock with trw 12.5 pistons to scat rotating assembly with icon 10.5 pistons is almost unbelievable almost a lb. very happy with scat’s products and service