Fig.: to raise no difficulties; to not worry about right or wrong

I'll make no bones about doing what I think is best for my family

Non mi farò scrupoli nel fare quello che penso sia la cosa migliore per il bene della mia famiglia

Little Charlie makes no bones about telling a lie to escape punishment

Charlie non si fa nessuno scrupolo nel dire una menzogna per evitare una punizione

Pay no attention to him! He makes no bones about boasting of connections with the richest and most powerful families in the city, but there is no truth to it!

Non fargli caso! Non si fa scrupoli a vantare legami con le famiglie più ricche e potenti della città, ma non è vero niente!

This idiom has its roots in the medieval practice of divination, which used bones to predict the future. If the future is plain clear, you don't need divination, therefore “no bones”, to know what will happen.
In the sense of "raising no difficulties" the phrase may refer to finding no bones in the soup, which is therefore easy to swallow quickly. Another possible explanation is that the bones are dice. Many gamblers make weird rituals before throwing the dice in order to win good fortune, others, who "make no bones" about it, just roll the dice once and throw them