You could stand to remove a few redundant edges, but otherwise, they're not too much of a problem... that's just normal triangulation. You can take out the edges by selecting them and hitting backspace, if that fucks anything up you can just undo it.
You're meant to be selecting the edges, go to the modifier menu, then selection, click the edge button, click the redundant edges (which will appear as those lines) and after selecting them press backspace...
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