After trying this maze in the laser cutter that had thin dividing lines, I realized that I would need to use a slightly different model.

The maze below worked out quite well. Now, I will probably work on adding the light that will illuminate if the maze is properly solved. 

Another issue that I faced, besides the border line thickness, was that the dimensions of my design were a bit off, so I had to pause the laser cutter and reset some of the settings. After that, it worked out great.