The grid lines should be a lighter-weight line than the x-y axis, but should not be so faint that the reader has difficulty finding them. What method are you using to create your tactile graphics? (thermoformed copy of collage? microcapsule paper? embossed image?) Perhaps the problem lies with the equipment being used to duplicate the copy. Is the thermoform machine set at an appropriate temperature? Is there not enough definition given to the grid lines on the Master (original) diagram page? Are you getting a dark enough image when you photocopy onto the microcapsule paper? Some developing machines produce a better-quality product on the microcapsule paper than others. There are many issues that could be causing the faint grid lines. I would need more information in order to adequately answer your question. Perhaps you are not producing the graphics yourself and an agency is not keeping a close watch on their quality control.
A carefully planned, and well prepared tactile graphic should have enough contrast in the types and strength of the lines that your student should not be having the difficulty that you describe. I do hope that you are able to find a solution.
BANA is responsible for publishing the approved copy of Standards and Guidelines for Tactile Graphics. That would involve getting quotes (or bids) to determine where to have it published. Timelines would need to be established with the publisher. The supplement of tactile graphics that accompanies the Guidelines includes samples of all the various methods of production and will be labor-intensive to reproduce. I believe that it is BANA's intention to post a print version on their website, but even that takes time to prepare the markup language for accessibility. Watch for details on their website.