If “in response” means replying back to tower on tower’s frequency, then no. After the lady on tower frequency told them about traffic (twice), they came in on departures frequency (it was a fresh contact, they started with “good afternoon, American 4 with you”) and said they have traffic in sight.

Edited after I rewatched the video:

1. Tower handed them off to departures.

2. They said bye and stopped listening to tower.

3. ITA veered left.

4. Tower noticed it and warned them, hoping they are still listening.

5. They were evidently not listening to tower anymore, and did not contact departures yet, when they noticed traffic themselves.

6. They greeted departures saying they see traffic, and veered left.

Later at 2:45 American said tower didn’t give them a heads-up. The fact that departures asked them about it could mean that departures thought they were still listening to tower.

Pretty sure the pilots have a second radio and could be listening to both departures and tower during handoff, but it’s unclear whether that’s routine. If they did it, they would have heard tower’s original warning.

> I believe their avoidance maneuver was a climb change.

According to the chart in the video, AA veered to the left. This maneuver started around 1:51 in the video, which is at least 10 seconds after tower warned them of traffic and instructed to stop the climb for the first time around 1:38.

I don’t know if they stopped the climb around 1:38. If we know for sure that they stopped the climb around 1:38 when tower told them so, then there is a good chance they were indeed still listening to tower and heard the traffic warning. If that’s the case, maybe they thought that stopping the climb 10 seconds earlier was insufficient (and tower was wrong about it).

Note that VASAviation's visualisations are not always 100% synched with ATC radio recordings, and the radio usually has gaps removed. It's a useful overview to see the tracks, but take the video's timing with a grain of salt.