How Critical Is Replacing Thermal Interface Material?

My motherboard died (the RMA replacement will arrive on Wednesday), and I was looking at the AMD CPU installation sheet that came with my processor, and I noticed that it says:

"Note: If the heatsink is removed for any reason, all of the old phase-change thermal interface material must be removed. Then, new AMD-recommended phase-change thermal interface material must be installed on the heatsink."

I of course did remove the heatsink and processor from my dead motherboard, before RMA-ing it, and I don't have any thermal interface material on-hand, do any of you know if this is a critical step or is more a "if my CPU starts overheating, apply thermal interface material then" step?