Blender have built in option for this which is called delta transform. Where no animation change is required, Just select your objects and then alt left click and drag the mouse in object properties in delta transform panel
This delta transform doesn't work with gizmo, I understand the add-on currently have flaws and I will work for a new/better version. But when you have 100 baked objects from physic simulation, and just wish to offset part of them left, or back-read, it's really not convenient to just alt+delta transform each x,y,z manually whereas an operator/gizmo facilitate artistic control.
Animation Transform Offset
Does not work on armatures only objects