I face this all the time since I fast very regularly. I am totally honest to everyone who asks about my weight loss or think I am sick. I tell them I am fasting with water only and why I am doing that. What people think is their business and your health is your business. I am by no means saying that you have to do the same. I have used excuses such as, I am on a juice fast, I am on fat only diet, etc. I also tell them the advantages of fasting or juicing, i.e. omg, I am getting so much junk out of my body, the detox is amazing, etc. which part is the truth.
You will be fine with weight loss below normal weight for your height. You will gain it back as soon as you refeed.