Well first it's helpful to know what the white deposit is. Like your teeth, orthodontic retainers can build up plaque and tartar. The white stuff is calcium left behind from saliva. Now if your child has been ultra-diligent about cleaning her retainer on a daily basis, the build-up has been minimal. However, if that were the case you wouldn't be reading this article.
Take, for example, my son's retainers, which are a bit different than the run of the mill retainer in that they are designed to widen his palette and jaw. His devices have a little gear in the center that is turned once a week to spread the retainers. Theoretically, my son is supposed to wear them 24/7 with the exception of meal times. The reality is that he removes them at lunch during school, stores them in his lunch box without rinsing first, then lets them fester there till after dinner when he lightly rinses and returns the retainers to his mouth. When I finally became aware of his habit I nearly choked. When I got a close look at those plastic devices I recoiled so hard I nearly got whiplash. You could have mined the calcium build up, they were practically growing crystals!
No amount of soaking in Efferdent seemed to rid his retainers of the scale. They were nicely deodorized however.
Then, being the organic, holistic, find a natural way to do things kind of mom that I am, I realized the solution to this calcium build up lay in my kitchen cupboard in the form of distilled white vinegar. I added one part vinegar to three parts water in a cup and dropped in the offending orthodontia devices letting them soak for 15 minutes.
Victory! In those short minutes the calcium had softened to the point that with a dental tool, I was able to scrape away the entire mass of disgusting white calculus. As a bonus, the vinegar acts as a disinfectant too.
Since this discovery, I make sure that my son soaks his retainers in the vinegar solution at least twice a week and that he thoroughly brushes them daily. We've not had a problem since.
While I wouldn't try the vinegar solution on dentures because the acidity of the vinegar may mar the finish on them, a denture brush works better on cleaning retainers than a regular toothbrush because the bristles are stiffer. Every little bit helps.