We have a relative who is a nun and she is about to celebrate a religious anniversary. We were going to give her a small monetary gift, but then we heard that she would just have to turn it in to her order. Is that true?
Quite possibly. As a matter of canon law, whatever a religious man or woman acquires by reason of individual labor or by reason of being a member of the institute belongs to the institute (canon 668). This is an age-old facet of religious life and is consistent with the fact that these men and women have freely chosen to live according to, among other things, the spirit of poverty and to be bound by its consequences. It also recognizes the fact that the religious institute is ultimately responsible for the material needs of its members.
Personal gifts such as you describe do not, strictly speaking, fall under the above canonical headings. However, many (my impression is most) religious orders have, also in accord with canon law, enacted special provisions whereby all members freely renounce their canonical right to own any property, including personal gifts. It is also possible for individual religious to commit to such a practice as a pious exercise (see again, 1983 CIC 668).
If either of these cases apply to your relative, as is apparently the case, she would, as a matter of freely accepted obligation, turn your gift in to her superiors. If you wonder whether such is the rule in your relative's institute, ask her. It is possible, even in cases of institutional or individual total renunciation, that a small gift from a relative would be "returned" to a religious for his or her reasonable use.
By the way, if your gift is freely given to show your love for your relative, it shouldn't be of concern to you what she does with it.