As a member of the quilt ministry at my church I can totally and completely understand your dilema. We make quilts for people within our congregation that are suffering from serious illnesses. It has been my experience that sometimes, regardless of how much help you offer, some people are just not really good at sewing or quilting. I am a co-leader with another lady and we have spent countless hours re-sewing blocks, pulling off borders, pulling off backs, etc. We just don't have the heart to tell the people there are problems with it. I think they probably already know but really want to help. It is a very uncomfortable position to be in because, obviously, we want our quilts to be durable and to be pleasing looking to the recipient. And, overall, it is a gift from our church.
There are some quilts that we have "put away" to be saved for the future and will most likely not be given out. It is so hard because these ladies are so kind with their time and are so grateful to be a part of our ministry! Sometimes we have found other jobs for them like putting ties into the quilts or coloring a bag that the quilt will be delivered in, etc.
In answer to your question I would probably try and pull the block apart and see if it's salvagable. On the flip side at least it is a block and not an entire quilt! If there is no hope you can discreetly "put it away". It most likely will not be noticed as missing.
Take care and God bless you!
Kim