Dealing with Audio Interference

Some time ago, I posted here a diagram / pics of a UPS kit that powers the home phone base station and charges 2 iPhones at 1A thanks to the detective work at Adafruit. Yesterday, I finally got around to assembling the last bit, i.e. building a connector between the board and the base station. I've never had to solder connectors before, so this was a new experience for me. Anyhow, it all worked eventually, with one quirk: Noise!

Specifically, if the base station is powered using the standard wall-wart (looks and feels like a linear power supply), the voice channels are clear as a bell. Power the base station using my rig and there is a lot of background noise - basically static. I presume this is EMI entering via the power supply as the noise does not change as a function of distance, etc. of the base station to the power supply.

What would be your suggestion on how to best fix this? I have a number of old external clamp-style ferrite cores lying around, so my first inclination is to add one, wrap the wires around it a couple of times and see what happens. Similarly, I'm also considering retrofitting a capacitor on the output side, even if Dimension Engineering claims that "It has integrated decoupling capacitors, so external capacitors are not generally necessary". If you'd add a decoupling capacitor, I assume you'd want a small 0.1uF ceramic unit to hold in the noise?

Can you have access to a scope?
It could be a ripple problem or perhaps a bad linear VCC. A scope will give you your answer

HugoPT:
Can you have access to a scope?
It could be a ripple problem or perhaps a bad linear VCC. A scope will give you your answer

No linear regulator - the switch-mode power supply doesn't feature one. I checked the signal out on a scope and saw a bit of ripple. Dimension Engineering suggested retrofitting a 1000uF capacitor, which seems somewhat counterintuitive - I would have thought an inline inductor would make more sense?