Many ribbons print well using a thermal ribbon printer ... grosgrain isn't one of them.
But wait! There's a bigger question to ask when considering personalized ribbon in conjunction with grosgrain.
What is more important ... using grosgrain ribbon or offering a personalized product?
It's been standard practice to use grosgrain in items such as hair bows, lanyards, and gift wrapping. Granted, it's a luxurious textured ribbon and looks classy. You should use it in your designs. But what do you do about personalization using your thermal ribbon printer? Even though you actually can print on this ribbon, the result is not satisfactory.
The preferred methods used to customize grosgrain are a hot stamper or a commercial printing machine. These produce a nice sharp image however, they come with a downside. You must order large quantities and/or purchase dies for logos and specialty fonts. You also need to wait for your ribbon to arrive. Contrast that to producing only the amount of ribbon you need, in any font or logo ... and for pennies. It's also ready immediately to incorporate into your designs.
Use the benefits of thermal ribbon printing to your advantage here. Try incorporating grosgrain ribbon into the same products but in a different manner. Use single faced satin as the customized portion and layer it over your grosgrain for a fabulous effect. Put yourself in the shoes of that little girl who is overjoyed to have a hair bow with her name on it. You see, her name is spelled "Jazimina". Her mom is standing by filled with love and appreciation because of the pure delight in her daughter's smile. Then think about how this circles back to your business.
You are the one that provides products that create such a positive emotional response. Is it really about the grosgrain?