What could this white deposit be in this little bottle of Tung oil? Does this affect the oil? Should I take any measure?
Assuming this is pure raw tung oil* this could be nothing at all to be concerned with, occasional clouding is just something natural to raw oils. But as I say in my Comment above you do generally see it only when the oil gets cold so I don't know why you're seeing it now.
I think ideally you should try to return this bottle to the shop and get a replacement that isn't cloudy. While you're there look at their stock of this oil and see if some bottles are clear and some are cloudy, which would be perfectly normal variation for a natural product.
If getting a replacement is not possible I would try warming the bottle in a bowl of warm water (about the temperature of hot bath water) and seeing if the cloudiness goes away. If the oil does clear I think you should have nothing to worry about using the oil but I have no experience with this in finishing oils, only in cooking oils where cloudiness is irrelevant.
*Processed oils don't exhibit this problem if it's what I think it is.