While printing the grill, I noticed that the hole in the background of the original grill is visible from different angles, as is the gap on the bottom of the grill.
I therefore closed the hole in the middle and extended the grill further down to close the gap.
To achieve the honeycomb style, I adjusted the following settings in the slicer:
Wall loops: 6
Top shell layers: 0
Bottom shell layers: 0
Sparse infill density: 30%
Sparse infill pattern: Honeycomb

I had to turn the grill background insert by 45° to align the honeycombs with the grill.
Thanks to @Prism08l for his great work!
The author remixed this model.
Closed the hole in the middle and extended the grill further down to close the gap.