ICE is an American institution, so the pronouns are used appropriately.
Otherwise, they'd have to replace the pronoun "their" with "Immigration and Customs Enforcement", or ICE again in the same sentence, and so on.
Pronouns are used as a substitute for the subject so that you don't have to use the same exact term repeatedly in conversation.
The pronouns following the subject all pertain to the subject until the subject is changed.
This is ENGLISH!