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This mesh is exported from a game, and everything is triangulated. The way the mesh is set up is 256 (16x16) squares like the one on the right in the picture below. I want to make it look like the square on the left, which I did manually, but doing them all manually would be about 16,000 faces.

enter image description here

The problem with using things like Tris to Quads is that each square I want to make is 4 triangles, while blender tries to make the diagonal faces which leaves triangles at the edges.

enter image description here

Also, the mesh is a landscape so using grid fill will get rid of the shape as far as I know. I'm not that advanced in Blender so I might be missing something, but I really need to automate this.

Edit: Just a side note, I have never seen them before, but when I import the game models they have blue lines. What are these?

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Select Similar

I think there cannot be an unique answer: there are multiple possible solutions to the problem of "grouping tris into quads". For example Blender is showing one of them, that cannot be said wrong in anyway. That's its automated way to solve the problem.

You'll have to write your own algorithm in order to specify what kind of index order should be followed while packing tris. Luckly, in the provided exmple you can take advantage of another tool: Select Similar.

As long as there is a recognizable pattern in the distribution of the triangles, as in your case, you can simply select all the vertices that are ruining your quads and dissolve them.

Pick one vertex in the middle of the "future" quad, run Select Similar command with "amount of connecting edges" option, then press X and choose Dissolve vertices

enter image description here

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