Typically the answer is “YES” the Soldier can be ordered to remove unprofessional information from a social media site.
While your actions may be well intended you have also ventured into a grey area. The Army is currently struggling with how to address certain events that occur on social media. It would be best to run your situation through your chain of command and have them get a legal opinion from the local JAG office. It would also be a good idea for the unit commander to establish a social media policy and have it approved by the local JAG. There is also a U.S. Army Social Media Handbook and ALARACT 014 2017 that might provide some additional assistance.
(1) Hazing. Any conduct whereby a Servicemember or members regardless of service, rank, or position, and without proper authority, recklessly or intentionally causes a Servicemember to suffer or be exposed to any activity that is cruel, abusive, humiliating, oppressive, demeaning, or harmful. Soliciting or coercing another to participate in any such activity is also considered hazing. Hazing need not involve physical contact among or between military members or employees; it can be verbal or psychological in nature. Likewise, it need not be committed in the physical presence of the victim; it may be accomplished through written or phone messages, text messages, email, social media, or any other virtual or electronic medium. Actual or implied consent to acts of hazing does not eliminate the culpability of the perpetrator. Without outside intervention, hazing conduct typically stops at an identified end-point.