The sunnah of using a tooth-pick

Islam lays unparalleled emphasis on oral hygiene. In addition to using the miswak at salah times, the miswak is recommended on several other occasions too.

The Sunnah of Picking the Teeth
Another form of oral hygiene in Islam is the encouragement to pick the teeth after meals.
Sayyiduna Abu Ayyub (رضي الله عنه) reports that Rasulullah (ﷺ) said:
‘How good is [the practice of] those in my ummah, who wash between the fingers and toes in wudu, [i.e, by doing khilal] and those who pick their teeth.’
(Musannaf Ibn Abi Shaybah, Hadith: 97 and Musnad Ahmad, vol.5 pg.416)

Tooth-picking
In the above and other Hadiths, we are taught to pick the teeth after meals.
In addition to causing decay, leaving food unpicked from the teeth also creates an odour which offends others.
(See: Faydul Qadir, Hadith: 3672)
The teeth are usually picked:
a) with the tongue,
b) with a finger,
c) with an object like the toothpick/dental floss/waterpik etc.
However, we are advised to not swallow the food particles that are picked with the fingers, toothpicks or other foreign objects.
This is not binding [i.e, not haram], but is indeed advisable. See the Hadith below:
Sayyiduna Abu Hurayrah (رضي الله عنه) reports that Rasulullah (ﷺ) said:
‘…Whoever eats and removes the [left over] food from between his teeth with his finger [or any foreign object, like a toothpick] should spit it out. What he removes [from the teeth] with his tongue, he may swallow. Whoever abides by this does well, and who does not, will not be sinful.’
(Sunan Abi Dawud, Hadith: 36, Sunan Ibn Majah, Hadith: 337 and Sunan Darimi, Hadith: 689 and 2132)
Imams Hakim and Dhahabi (رحمه الله) have declared this Hadith authentic (sahih).
(Mustadrak Hakim, vol. 4 pg. 137. Also see: Sahih Ibn Hibban; Al-Ihsan, Hadith: 1410)

One reason for spitting what is removed with a foreign object is due to the possibility of it having blood on it. [The consumption of blood is unlawful].
(Badhlul Majhud, vol.1 pg.23)
The above should be done with the intention of following the noble teachings of our Beloved Nabi (ﷺ).
Every sunnah is filled with immense barakah and benefits.
Let’s abide by this, and add to the number of sunnats that we practice upon.