Counter-offers are flattering and frequently regretted.
Ask the uncomfortable question
"What changed today that could not have happened three months ago?" The answer tells you whether this is a genuine correction or a stopgap while they plan.
Separate money from reasons
Most people leave over management, growth or workload. If those are your reasons, more money changes nothing and you will be having the same conversation in six months.
Consider the after-effect
In some teams, accepting a counter-offer marks you as a flight risk and affects future opportunities. Not everywhere, but worth weighing honestly.
Common questions
Should I ever accept a counter-offer?
Sometimes, if the reason you were leaving was genuinely pay and the increase is properly documented.
Is it unprofessional to use an offer as leverage?
Getting a competing offer and discussing it is normal. Manufacturing a fake one is not, and it is easily discovered.