Some people like their food too much to share it with anyone :) but the idea that the food on one's plate must not be violated or as one user described— tainted—by someone else's mouth is not totally outlandish to English native speakers.
Normally, a person drinking straight from a bottle of water will not offer to share it with a friend or a coworker. And some people will visibly recoil if you suggested they taste an ice-cream which you'd already licked. The most likely reaction would be eww; gross; yuck and a few will add: “It's got your germs all over it!”
However, among close friends it is acceptable to take a taste of that person's beverage especially if it is alcoholic. And men will bond by sharing the same bottle of beer together. Sharing food or allowing friends and family members to taste something from your plate using a fork is very common, the vast majority of European and North American speakers find this behaviour totally normal, and would be surprised to discover sharing food in this manner is taboo in different cultures.
Therefore if the OP wants to convey the meaning of Jootha in English he will have to use that word and give its definition, and more importantly, explain that it is part of their culture. This may be fine in a relaxed situation over dinner but with a complete stranger I can see how this solution might be viewed as being intrusive and time consuming.
In a situation where a short phrase will have to do, I might say any of the following with an almost apologetic tone of voice and shrugged shoulders, just to convey that you understand the listener might find this odd but you are powerless to do anything about it.
- I'm sorry that food has been touched by someone else
- I'm sorry, but I cannot share the food on my plate
- Please, don't touch my food.
- My culture forbids me to drink from the same bottle, glass, etc.
I would strongly advise against using the term ort, a word which is becoming increasingly rare as confirmed by this Ngram. Results from Google Books show many false positives, such as last names of authors, acronyms, and the name of a children's book character. The most common and easily understood expression is without doubt leftovers.