Leave them there. It is unsightly, but the leaves are still useful to the plant.

I lost my first few noid store bought Phal's by drowning them. The in-medium Phal roots will keep trying to absorb water to send to the leaves past the point where the leaves can hold water. The in-media roots then usually rot. They need to dry out some and to get air. Many windowsill growers find that Spag is a treacherous potting medium. The shipper uses Spag to keep the plant alive and in bloom over the period that it is in transit when it cannot be watered. (Some of us claim that it is used to insure that the plant will die and one will go buy another one in bloom!!!) So, as a windowsill grower, over the years, I have found that replanting a new grocery store purchase in a fir bark mix after the blooms fade will help insure the plant lives to rebloom.

People offer advice based on what has worked for them. Be sure to pair the suggestion with the growing location. Bruce has done us a great favor by including the "I grow my orchids:" tab.