You CAN block other phones (and restrict range) -- it's not pretty but it works if you have neighbors on only one or two sides of your house or apartment.
Create a five-sided Faraday cage out of a cardboard box and aluminum foil, and put your Network Extender in the box, with the open side facing away from your neighbors. I can attest that this works -- behind my homemade Faraday cage I get absolutely no Extender signal. Where the open side of the cage is pointing, I get normal signal. Point the open side of the box/cage where you want the Extender to broadcast. The closed, back of the box should be facing your neighbors -- they will be unable to connect
You will need to use the GPS extension cable that came with your unit. Pull open the top back cover and unplug the GPS sensor from the Extender. Mount the GPS sensor high outside a window with double-sided sticky tape. Connect the GPS extension cable to the GPS sensor and route the cable into your house (the cable is slim enough that you can close your window on it). Route the GPS extension cable to your Network Extender.
Find or create a cardboard box the size of a shoe box, with an open vertical side. Cover the outside of the box with aluminum foil, and the inside as well. Make sure the foil pieces are folded over each other: no gaps. You've just made a Faraday cage! Position the box long side vertical, and cut a small hole in the bottom. Unplug your Network Extender from all cables, and push the three cables up through the small hole GPS extension, Ethernet and power -- position the Network Extender deep in the box and plug in the cables. The GPS extension cable plugs in to the top of the Extender. Squish some aluminum foil around the hole where the cables come in to the box. Position the black antenna on the back of the Extender against the back of the box as deep as it will go, it's OK if the front of the Extender sticks out the front so you can see the LEDs.
Some facts:
On your Verizon Wireless portal, you can tell the Extender to /prefer/ your family phone numbers, but this is hardly functional. In practice I find that all mobile phones can normally connect to my Network Extender even to the point of restricting my own phone which is Preferred on the Verizon portal. I've even found this to be true for phones on a non-Verizon plan, AT&T phones can roam on Network Extender, including voice calls as well as 3G data. On several occasions my Verizon LG G2 has told me that my Extender has no free channels and cannot make a voice call. Rebooting the Extender allowed me to eventually make my call, but the Extender takes a long time to boot (5-10 minutes) so this is annoying. There are seven channels available on your Network Extender; six for phones (concurrent), the seventh is for 911. If Android, look in your notification bar: I see a little house icon when connected to Extender.
While you cannot control who can use your Extender if they are in range of your signal, you can monitor how much Internet traffic is being used by the Extender, and then configure QoS to limit the total bandwidth used by Extender. Find your Extender's MAC address, and create a DHCP reservation on your home router/firewall. Once the Extender is always on a known IPv4 address on your private network, you can monitor traffic to/from that IP address, and create QoS rules -- my Extender is limited to 512Kbps up/down. This allows it to make flawless voice connections, but limits the amount of 3G data that can be used.