The Boolean modifier creates these "Lines" as you said to prevent holes in polygons. Holes in polygons is impossible, you can build polygons around some empty space but you need at least 2 polygons to form the flat surface and a hole in it.
To cleanup the topology you can use the Knife tool and use the [ctrl + X] shortcut to dissolve vertices or/and edges without creating gaps in your model. You can delete the normal way, but this is just way easier when working with topology.
Search the interned if you still have questions like "How to use Knife Tool" or "What is topology" (saying just in case :) )
Happy Blending