The answer is non-trivial. To investigate this, you should consider this question from two points of view, your own and the questioner's.
- From your own, ask: If I ignore a thought, where does it go?
- From another's, ask: Is ignoring a question not itself an answer?
Once an something becomes part of your consciousness, you have no choice but to respond. So, how does one properly respond? Zen looks for precisely the same thing that Aikido does:
A clear, spontaneous, and appropriate response to your circumstances that restores harmony.
That statement, though, has many land mines, and in my view is almost universally misunderstood. My goal for my Aikido teaching, besides training an effective martial art, would be to find a person or two who could clearly see the meaning this, perhaps even better than I can.
The first koan I was given was very succinct:
A student asks Master Yun-Men, "Not even a thought has arisen; is there still a sin or not?" Master Yun-Men replied, "Mount Sumeru!" Why did the master answer this way?
If you see why Master Yun-Men answered the student this way, you will also see why this study is relevant to Aikido practice.
I am happy to help to whatever extent I can and to point you to others where I cannot.