So the 4 point GotG ATA says "Powers possessed by characters using this team ability can't be countered. This team ability can't be used by wild cards."

How does this interact with Pulse Wave? For example, if someone with the above ATA and Invulnerability is attacked by Pulse Wave does the damage get reduced?

Pulsewave ignores your powers, instead of countering them. So this ata doesn't help against pulsewave but is useful to help against outwit

Pulse Wave does not Counter anything. Pulse Wave ignores. Those two terms are not interchangeable.

So Pulse Wave would still ignore their powers.

Here is an amazing article on Pulse Wave written by sn incredibly handsome guy
http://www.hcrealms.com/forum/showthread.php?t=519913

Excellent. Thanks for the help, guys. Follow up question:
"Opposing characters can't use defense powers when they are the target of Iron Paladin's close combat attack."

Where does "can't" fall into the "counter"/"ignore" argument?

It's different from both of them.

Correct. Can't/Cannot Use is just that. The character simply cannot use the power. It is neither countered nor ignored.

Also, realize that powers like that simply refer to the power showing in the Defense slot not a "defensive" power. For instance you could still use Shape Change or if you have a trait that grants Impervious you would still be able to use Impervious since it is from a Trait and not a power showing in the Defense Slot of the dial.