Destination Gateway Genmask Flags Metric Ref Use Iface
0.0.0.0 10.2.0.1 0.0.0.0 UG 0 0 0 eth0
10.1.0.0 0.0.0.0 255.255.255.0 U 1000 0 0 eth1
To reach the 192.168.1/24 subnet, the routing table should have the routers reachable IP as the default route (0.0.0.0) but instead it has 10.2.0.1 which is not an interface on the router.
On the remote machines routing table, change the default gateway (0.0.0.0) route (currently set as 10.2.0.1) to 10.1.0.1/24