If we assume the implementation of this button is similar as Android's Home button, we can use the same approach to override it.
For example, here's an activity declaration with an intent filter to receive a MAIN intent when the Home button is pressed:
<activity
android:name=".MainActivity"
android:launchMode="singleTask"
android:excludeFromRecents="true">
<intent-filter>
<action android:name="android.intent.action.MAIN" />
<!-- The following two intent-filters are the key to set homescreen -->
<category android:name="android.intent.category.HOME" />
<category android:name="android.intent.category.DEFAULT" />
</intent-filter>
</activity>
In case you need, there are plenty of discussions for the Home Button case.
Then, you would need be to figure out what are the action being used for your button and then use a very similar piece of code on your activity declaration.