If she's close to delivery she's not likely to care and will mostly be resting anyways. You do want to watch though because if she does decide to chew out, you've got a pregnant rat loose in your house with a litter on the way....not a situation I'd want to have.

If you hit Home Depot you can get a small roll of 1/2" hardware cloth for that lid for about $5.00 and then another $2.00 or less for a bag of zip ties (or just use some wire to secure the mesh to the lid).