Could you upload a screenshot or two of the scaled-up TileMap being used as your background? As an experiment, I tried to replicate what I think you're running into in a sample project. Using an incredibly small (30x5 pixels) graphic I had lying around, I tried seeing if turning the Filter option in the import settings for this graphic would have any effect on the cells that have been drastically scaled up.
Here's the graphic I'm using for the TileMap:
Here's a screenshot of the scene using the graphic with Filter turned on:
Here's a screenshot of the scene using the graphic with Filter turned off:
I up-scaled my cell size to 32 times their original size so it'd fit nicely in a default 2D project space.
Notice how the super up-scaled graphic looks awfully blurry with Filter turned on. But then, turning Filter off gives us sharp pixels.
"Works on my machine" is never a satisfying answer so I feel like I'm not fully understanding your problem yet.