It is one of the companies that..
Removed background music from its stores.
Removed background music from their stores.
It is one of the companies that..
Removed background music from its stores.
Removed background music from their stores.
Technically, if the operation of the stores is subject to one legal entity, say Walmart, then the operator of the stores is singular, and thus the pronoun that is grammatically and legally correct is “its.”
If John owns one house where he lives from May through December and another where he lives from January through April, we say “His houses are in Connecticut and South Carolina” rather than “Their houses are in Connecticut and South Carolina.”
HOWEVER, speakers realize that the behavior of large corporations is in reality the result of behavior and decisions of many people; although hierarchical, corporations and governments are cooperative associations. Thus, the use of plural pronouns is common in many situations involving governments and corporations because speakers are addressing the human reality rather than the legal formality.