Verses 20 and 21 deal with the continuing concern with the priests of Noah. Limhi has his people vigilant for them for two reasons. The first is that these priests are the direct cause of their current level of distress. Presumably, the finding and punishment of the priests of Noah would demonstrate with finality the innocence of the Limhites in the conflict over the oath/treaty. That should diminish the anger of the Lamanite guards towards them, though it would not change the conditions of the original treaty.
The second reason is that the priests of Noah have been raiding the Limhites. How does Limhi know that it is the priests of Noah and not the Lamanites? He does not (unless they had been seen, which is not disclosed in this record). Nevertheless, he may readily surmise that the Lamanites have no need to steal, as they are receiving a large tribute already. Thus the only ones with true motivation for theft would be the priests who would be in need, seeing that they have a much smaller population and a lesser base on which to live. Since those priests would not have had time to plant and grow food, their theft of grain is completely understandable.