The service members were treated in Iraq, or at military health centers, including Landstuhl Regional Medical Center.
Violent clashes between Iraqi security forces and anti-government protesters also continued to seethe overnight.
Four protesters were shot dead as riot police stormed protest camps across the country.
Germany resumed training in Irbil on Sunday morning together with its partners.
Pro-Iran channels broadcast images of a gallows, with a puppet in the image of President Trump swinging from a rope.
Whether the troops could receive the Purple Heart for injuries as a result of enemy action is under review.
Since mid-morning on the Muslim day of prayers, loudspeakers blasted “No, no America!” at a central square.
An early test will be a “million-man” demonstration against the American presence scheduled for Friday.
The 82nd soldiers deployed to Central Command's area of operations Jan. 1-4.
The exact number of troops flown to Germany was not immediately clear, but officials said it was a small number.