Remote IP phones are clearly the way to go, although they do require a little more work, at least initially... And would depend on if there is a VPN in place or not... If there is, assuming sufficient bandwidth and network performance, you can add a route from their subnet to the voice VLAN and just put the phones in Teleworker mode and punch in the IP address of the 3300.
If there is not, then a Mitel Border Gateway is the way to go. The upfront cost is higher, a server, licensing, static public IP address, but in the end this is a very efficient, secure, and powerful way to manage remote phones anywhere in the world. Honestly, copper/analog leased service is a dying thing, where I am it is difficult to get in many places since fiber to the home is so predominant and IP connections are so cheap (like 200M down/30M up and 250 channels of HD TV for $65/month in the rural areas around town). MBG also has some neat features like acting as a SIP Border Gateway, opening up possibilities of SIP trunking and SIP endpoints off the Mitel as well, which can significantly lower operating costs.
Now is a good time to plan this out and start implementing, since in the future this type of service will become a thing of the past.
We have large "campus" type environments, with multiple offices across the city, around 1000 phones scattered in 20+ locations with 10 controllers in a cluster and about 100 remote phones, it works exceptionally well. Mitel clearly has this technology down, I would suggest a meeting with a competent Mitel vendor to discuss options about migrating away from this type of analog service and moving to IP, if not for just this situation but to future proof your telecommunications infrastructure... and leased lines are not cheap (at least not around here).