Depends on the radio frequencies used. This dish is designed to look at relatively low frequencies -- 6mhz to 30mhz. So I imagine that any potential new far-moon missions would probably just avoid those frequencies. These frequencies wouldn't be as useful as they are on earth anyways, because there's relatively low bandwidth, and there's no useful ionosphere to bounce signals are for long-range propogation like there is on earth.

Edit:

However, on the other hand, there could potentially be a lot of unintended low-frequency broadcasters -- microchips, etc. So I imagine there would still be a need for hold-out zones, but they'd probably not be as impactful as there are on earth.