Network Tunnels

We currently have the following tunnel  for our two locations  (A and B) and it is currently working. Some code in the tunnels was removed for simplicity. These two locations were very closed so we have a direct Ethernet link from one location to the other.  However, now one of the locations is been moved a few miles away. So  for us to  connect our two network locations, we will need to use another company network that we do not managed.   Is there any way for us to connect through this company network still using our tunnels?   or will we have to replace our configuration?

 
Location A  router A

interface Tunnel20
   
 ip address 10.0.0.5 255.255.255.252
   tunnel source GigabitEthernet0/1  
   tunnel destination 192.168.0.6

interface GigabitEthernet0/1
   ip address 192.168.0.5 255.255.255.252
---------------------------------------------------------------
Location B router B

interface Tunnel20  
 ip address 10.0.0.6 255.255.255.252
   tunnel source GigabitEthernet0/1  
   tunnel destination 192.168.0.5

interface GigabitEthernet0/1
 ip address 192.168.0.6 255.255.255.252