I'm going to say air is getting in. Which may mean that you didn't have a duff pump in the first place! 
It will be, if it is a leak, on the supply side from the cooler to the reservoir or reservoir to the pump. It could be a split at the jubilee clip or a pin prick in the pipe.
Look to see if there is any fluid at the end of the pipe, clean off and recheck.
The noise is worse on lock as that is when the pump works hardest and goes after a few seconds because it is bled into the reservoir.
I could be wrong! 
__________________
Conan (the Librarian)
Watch it if you dare
Currently,
2000 S8, Merlin Purple, Leather Pack 1, Winter Pack 1, SPAX adjustable suspension, AP Racing 6 pot front caliper, 385mm fully floating disks, EBC Yellow Stuff Pads, Black Diamond grooved rear disks and predetor pads, D2 Doctors Brake Block.
1997 4.2 A8SQ - the Projekt. 12 years and ongoing!
1997 4.2 A8SQ - Ming Blue. Restoration sat waiting; saved from the Scrapyard
2003 C5 Allroad 4.2Q - Cobolt Blue. Towing car. Laid up awaiting manual conversion.
2005 C5 Allroad 2.5TDi FE - Grey - Workhorse.
2015 Q3QS SLine - Daytona Grey. Lots of extras! Long Haired Admirals cutter.
Previously
2003 C5 A6 1.9TDI FWD - Loaner from D2 Doctor Lifex
1997 S8 - Ming Blue. Loaned out and written off. I loved that car. My first engine swap after cambelt failure.
1996 4.2 A8SQ - Ming Blue. 178k on a cambelt! Trader's 8. Delivered to A8Parts at Lifex.
2003 2.8 A8SQ - powder blueish. Fill in for a while. Sold on.
1998 1.8T A4 Avant FWD. Ming Blue (there's a theme here), PEX for the 97 S8.
And a list of non VAG going back 40 years before I saw the light. 
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