In some cases, like in the ground wire in your electrical panel or the ground wire running inside to be earth grounded via your water supply, it is often thick bare copper. This is where I mentioned it can start to get a bit more complex. When in doubt, hire an electrician.
In your case, you can easily keep it simple. Run a new one, use the same type and gauge (or thicker) and reconnect it to EXACTLY where ever the old earth ground was connected to.
I say "exactly" because, yes, it is most likely the bar in your electrical panel but it could also be something else. For instance, there may be a junction box somewhere between the outside rod and the panel. Things like water meters have to be bypassed in that type (water source grounding) of scenario. It is also possible that the ground rod and wire you cut is for a specific purpose other than your household power. As mentioned, if a phone installer can not access the existing earth ground, he may drive a rod specifically just for the lightning protector for the phone system. It might not touch your electrical system at all.
Anyways, this is delving deeper than my expertise goes so hopefully I'm being paranoid and overcomplicating. An A to B rewire should be very simple as long as you trace it out carefully ahead of time. If you have the slightest doubts, check with an electrician, of which, I am not one.
