If you call Dish and give them the Joey receiver ID, they will send you a pre-paid UPS box with sticker so you can send it back to them.
You are correct to electrically terminate the old cable as it will mess with the signal degradation and impedance of the 75 ohm coax.
There are two ways to do this, either at the old Joey end in which case you would just need a barrel connector and a 75ohm terminating plug.
The terminators are dirt cheap, you used to be able to get them at Radio Shack but I still think Home Depot or Lowes might have them.
But either way, you can get a pack of 10 for about $5 from Amazon Prime.
Amazon product ASIN B000AAN76Y
I you have an loose or unterminated coax lines, you really need to put a 75ohm load on it so it doesn't 'leak' out signal.
So if you can trace the cable back to the block where it comes from, simply unscrew it and screw in the terminating plug.
If you don't want that hassle, you can just get some coax barrel connectors (I know HD has those). Screw one end into the coax and screw the terminating plug into the other and you are done.
If you are lazy and just want to get it all delivered, here is the link from Amazon for the barrel connectors (you may even have some laying around).
There are tons of them on Amazon for just a cheap, just search on 'cable barrel connector' But if you them make sure you get the ones with the BLUE center insulator as Dish also supplies a higher power over the MOCA connection.
Here is an example of some. If you go to HD, then don't get the ones that are white of clear in the center, make sure they are the blue ones.
Amazon product ASIN B01E6ZENCK
These are 10 for 8 bucks but they also have packs of 5 for 5. Personally it's good to have some laying around in case you need to extend and existing coax cable.