Well, you could try something like
iptables -P INPUT DROP
iptables -A INPUT -m state --state RELATED,ESTABLISHED -j ACCEPT
so that the machine can connect to other computers but doesn't respond to any inbound connections. You can add more rules to only allow connections from certain hosts, but anyone watching traffic on a router might be interested that there's traffic coming from an IP that doesn't seem to exist. Why do they need to hide the computer?