This committee should inform the president of its recommendations.
The reason for the selection of this possessive pronoun is that "this" is in singular form and has to agree with the possessive pronoun that we choose.
Normally, collective nouns, such as committee, refer to a group of people and it is acceptable to refer to them by both singular and plural pronouns. Here, though, it sounds more natural to use "its" instead of "their" because of "this" which is in singular form.