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Miez doesn't like walking on the grille
(i.imgur.com)
My cat slowly walking on, but then jumping over the grille until she finally walks around it.
A simple strip of cardboard or narrow board would be nice for her to walk on and still let the grate do its grate-y thing.
You're right, but that's a nothing hop for a kitty. Cats utilize vertical space more than we do usually. It's one reason they get more exercise indoors than dogs can. Unless she's disabled, in which case by all means accommodate.
There really is no need as she could simply walk around it without any inconvenience (the grille isn't as wide as the doors). She just prefers hop over it.