As long as the ink hasn't set in the clothing too long then yes toothpaste will get ink out of clothes.
To get ink out of clothes using toothpaste you apply the toothpaste to the ink on the clothing and allow it to sit for a few minutes.
Then run the clothing and ink stain under cool water and gently rub the toothpaste into the fabric while doing so.
If that doesn't work then you can try using vinegar to get ink out of clothing.
Yes vinegar will work to remove ink from clothes.
Soak the ink stain on the clothes in some vinegar and allow it to sit for 5 or 10 minutes.
Then make a paste of cornstarch and vinegar and rub the cornstarch and vinegar paste into the ink stain and then let the paste dry before washing the clothes.
If you have a really stubborn ink stank you may need to fill a bowl with some a cup of vinegar and the rest warm water and place some baking soda into the bowl as well.
Then agitate the clothes by hand and allow the clothes to sit in the bowl of vinegar, baking soda and water overnight.