I asked 'Ā'ishah, saying: What did the Prophet (may Allah's peace and blessings be upon him) use to start with upon entering his house? She said: With the Siwāk (toothstick)

It is generally permissible to use the Siwāk at all times, but this is even more confirmed on the occasions recommended by the Legislator, including the following: upon entering the house, when praying, when performing ablution, after waking up from sleep, and when having a foul breath.
Showing how keen the Tābi‘is were to ask about the Prophet's states and the ways he adopted to follow his example.
Learning knowledge from those who are qualified and who know more knowledge, as here ‘Ā’ishah (may Allah be pleased with her) was asked about the state of the Prophet (may Allah's peace and blessings be upon him) upon entering the house.
It shows how the Prophet (may Allah's peace and blessings be upon him) treated his family kindly as he used to clean his mouth upon entering.