Conifold's point, his caution, about subjectivity is well taken. What might usefully be done, however, is to reconstruct the moral thinking that would make A's reaction intellectually coherent. What view of morality, regardless of whether I or anyone else accept it, makes sense of this reaction ? This can be done, I think but could be wrong, without undue or any subjectivity.
A is inclined to what Sir David Ross calls 'beneficence' - making the condition of others, in this case B, better in respect of pleasure (or some other metric). A also, however, appreciates gratitude (which also appears in Ross). B does not reciprocate A's beneficence with gratitude.
If A just practises benevolence because s/he feels like it, it is hard to see A as a moral agent as distinct from just a nice person to have around. If B's ingratitude merely pains or irks A, then it's just a psychological matter how A reacts.
If, however, A believes that s/he is acting morally in practising benevolence, then benevolence remains a moral requirement regardless of B's ingratitude. A did not act benevolently for any return, and receives none : morally B's ingratitude then is irrelevant to A's benevolence. The moral requirement of benevolence remains.
Suppose, too, that A believes gratitude to be a moral duty. A can perfectly well point out to B that B is failing in this duty.
None of this expresses my opinion about how A should conduct her- or himself. But it does outline a coherent scheme of moral thought in which the situation described in the question is intelligible.
The references to Ross are from 'The Right and the Good' (Oxford, 1930), 21. And I am not making a plug for Ross.
On a contractarian view of morality, which assumes and requires reciprocity and mutual benefit, benevolence and gratitude can be seen as paired requirements. If A is beneficent to B but B shows no gratitude, including no reciprocity, then A can claim that the contract has been broken and that B's ingratitude releases A from beneficence. David Gauthier's 'Morals By Agreement' (1986) explores the thinking that supports such a view of morality. Not a plug for Gauthier either.