The ones on the Martelli mats are mostly accurate. I use the mat as a rough measure and to keep the bottom of the fabric straight.

If it's just from cleaning then you probably can re-mark. If it's from cutting, use a different spot until it's time to get rid of the mat.

The light blue lines seem to leave residue on a cloth when you clean it. (I've got overspray from 505 on my mat)
Even just plain water seems to pick up the light blue. I did find one brown fabric marking pen that put a mark down that won't come off without a chemical. I'd bought the pen many years ago for an autograph quilt and it still has ink. I was marking lines to practice FMQ when I accidentally touched the mat.

This pen did not bleed and the mark isn't coming off unless I use a solvent. It's made by Stabilo and any good art store should have it.

Me, I would use a fine tip sharpie marker and a metal ruler with a 90 degree L and remark the lines.

what brand is it? you may be able to get a new one from the manufacturer!

Have you tried a regular ball point pen? I have some ink marks on my Olfa that have not come off after several washing/soakings. I tried rubbing alcohol, dawn, and even bleach on a qtip. They have been there for years. They are light marks, maybe where I went off the paper when tracing something. Looks like they just melted into the mat.