However, it would seem that there is still to room to be lenient with the above. It’s true that it’s forbidden to give presents on Tisha B’Av, however, the Hisorarus Teshuvah says that one is still allowed to send food to his friend to ensure that he has what to eat after the fast. The reason this is allowed is, that one isn’t doing this for purposes of friendship, and one is doing it simply to ensure that his friend has what to eat and is a mitzvah of tzedokah and gemilas chasodim.
The Kaf HaChaim (554:91) rules similarly and says, that one is allowed to send a present to a poor person, especially if he is a talmid chocham - not only is it not an issur, but it’s also a mitzvah as well.
We see from these poskim, that if the present is not being given for greeting purposes, but is being given for some ulterior motive, then it may be given even on Tisha B’Av. (Based on this logic, the Shu”t Divrei Malkiel 5:237 allows one to send mishloach manos to a rov on Purim even if the rov is an avel, as it is being given to pay up a debt of hakoras hatov to the rov, and not simply as a present.)
