Let them say their piece
Acknowledge the feeling before you defend the change.
Explain the reason in one or two lines
Give the real reason, such as cost, safety or fairness, without corporate wording.
Say what stays the same
Point out what is unchanged, so the change feels smaller.
Offer a way through
If there is flexibility, such as a longer notice or an exception, say so.
Hold the line where you must
Be kind and clear when the rule applies to everyone.
Collect the feedback
Tell them where you record it and what happens to it.