Elbow grease.

Seriously, "safer" stuff like Roundup (glyphosate) could theoretically just kill the grass, but all it takes is a sudden lapse of concentration or a gust of wind and that bell pepper near that tuft of grass you wanted to spray is hosed.

Are you sure the grass is growing through the landscape fabric or has your garden simply been seeded by bermuda grass?

what AJBB already stated: ELBOW GREASE ... those grass killers will kill your veggies ... when prepping this fall for our second season, dig up the beds and lay newspaper down on top of the landscape fabric then add back the soil ... you can also prep future beds by laying thick BLACK plastic over the top of the beds for a few months over the summer, this will kill off all remaining grass/weed seeds as the heat builds up, like hot composting ...

I definitely would recommend buying bulk of landscape fabric or some type of burlap. This will help eliminate the grass and weeds that keeps getting in the way of your veggies. I buy mine from Gempler...good price & good quality. I'll link it below.

Hope this helps!

Here is a link that might be useful: Landscape Fabric

I just keep pulling it up and applying thick mulch. Using a drip system or soaker hose helps, too since the whole bed wont get wet on top.
Mine is coming through several layers of newspaper and the raised bed dirt. It does seem to gradually be getting a little better. I pick the grass every day, as soon as I see it.
I'm making two more beds and doing a thick layer of cardboard, newspaper and pine straw on the bottom.

I kill bermuda grass in beds by pouring Roundup in a jar then using a one inch foam craft brush (or smaller) to paint the liquid onto the blades of grass. It's slow going but works well without causing problems for the other plants.