I thought if I had this complaint, others did too. So I took pictures of the way I remedied the problem. If you use scissors, use small, sharp ones, and for the love of all that is holy to you, DO. NOT. CUT. ELASTIC!! For this to work, you must cut ONLY THE FABRIC LOOPING AROUND THE CONNECTION. The fabric that makes contact with the pop-top-clip is all you will remove, unless you opt to remove the cushioning fabric so you can adjust the straps shorter. That's up to you. Do not cut the seam in the bra strap or your bra will be of no use. Again, if you remove cushioning fabric, cut ONLY the outer fabric, NOT the elastic of any kind.
Here's your idiot clause/disclaimer:
Please use caution when handling any sharp object. I used a seam ripper. If you use scissors, do not cut the elastic of the bra straps. I am not responsible for blade or seam ripper placement when you do this, as I am not there to physically guide your hand directly to avoid rendering your nursing bra useless. Pay close attention to where you cut, and how you cut. If you lack the skill and confidence, you can hire your local tailor and show this blog post to explain what you want done. If you lack common sense, then definitely hire a local tailor. Come to think of it, if you lack common sense, child-rearing may not be an appropriate life for you.
As you can see in the after/before picture, there is significantly more room for the clip to operate. I don't know who designed this bra, but they didn't think very far in its wear and use when they thought of these things. It makes me think a man with no experience or exposure to breastfeeding and the logistics it requires had a hand in this detail.
The bras adapted here were Motherhood Maternity brand, molded cup, non-underwire bras purchased at Destination Maternity in the Spring of 2013.