I have taken my eyedrops/cleaner that has peroxide in it and decanted it to another bottle that I have sterilized and labeled with an innocuous content. Never had an issue.

However, with the new enforcement of LGA/baggie rule, I will once again take out my baggie in order to try to avoid a check of the items in the baggie, at least for the time being.

As an aside, why does TSA not realize that the more they give screeners to look for, the higher are the chances that something truly dangerous will be missed?