I think I understand now.

In this example, it looks like we select 2 nodes in the tour:

We have (A, B, C, D, E, F, G, H, I, J).
The nodes we select are C and H.

(A, B, C, D, E, F, G, H, I, J).

Since this is a route, we can say that C is connected to D and that H is connected to I. (Basically the next node)

So now we know what our selected links are:

(A, B, C, D, E, F, G, H, I, J).

From this, we can deduce the internal sequence:

(A, B, C, D, E, F, G, H, I, J).

If we reverse this internal sequence, we get:

(A, B, C, H, G, F, E, D, I, J), which is better (we eliminated the cross).
 

This whole time I was thinking about selecting two links from the world:
Link1 = Link with agent_1 and agent_2

Link2 = Link with agent_1 and agent_2

Then swapping Link1's agent_2 with Link2's agent_2

In this case, I'm assuming we reverse the internal sequence, keep it if its better, and then let the engine generate the links from the tour (rather than editing links directly).