Yes very important.
I had gore tex gloves given to as a chrismas gift, 3 years later they leaked. So i asked the one that gave me the gloves for the receipt, but they didnt have it no more.
I tought, no problem, tell me where you have bought them, and i will contact them to get the receipt, but after checking the shop went out of business 2 years ago, so no receipt.
Nor the manufacturer or gore tex will do anything without the receipt.
So now i trew the gloves away, and bought me some cheap other tex gloves, that i will trow away in 3 years.