How many phones do you have at the remote site? If you have multiple phones, is it happening with all of them or just one of them? Have you tried resetting the phones to factory default? And do they have the latest firmware?
I don't know what kind of functionality is built into the Linksys VPN routers, but I'd imagine that it's not particularly function-laden in terms of diagnostics. What you can try to do to see whether the traffic is making it back across the VPN tunnel is to set up a hub that connects to a PC running Wireshark, a remote site phone, and a connection to the Linksys. Try making and receiving calls and seeing if you can see SIP and RTP traffic flowing back from the main site. If you've got a way to watch the traffic from the router, that would make life easier.
Also, do you have a different brand of VPN routers that you could try? I've seen it happen where sometimes between all of the encapsulation/decapsulation, firewalls, and NAT translation that sometimes the SIP and RTP traffic can get mucked up traveling through the internet. If that's the case, and it'd take a good deal of in-depth study to find out, you'd have to contact Linksys/Cisco and let them know. Not saying that that's what is happening, but it's a possibility.