Chad, what bad taste your customer had! I love your extremely HIGH-quality starfish. Hopefully you'll be able to enjoy them again someday! I personally like the grooves - they add dimensionality.
I make these guys too, in soft glass, using the same flattened-fritted-gather-cut-into-five-"petals" technique that Jodie described, except I do it lollypop style, not maria-style. This technique also creates major groovage. I pre-shape the "petals" into rough points using micro-masher tweezers bent into a 45% angle (my favorite tool!), then pull them into slightly twisted points (the slight pinwheel twist at the tip helps hide my inevitable assymetry!) The "petal" attached to the punty becomes the loop-point. I just call them "stars" - customers interpret them as they like.
Forgive the bad photo quality, it's just from my inventory pics.