Pasta del Capitano Antitartaro is best understood as a daily brushing toothpaste for helping keep teeth cleaner between brushings, not as a way to scrape off hardened tartar at home. Its pyrophosphates are included to help reduce the attachment of mineral deposits to the tooth surface, while hydrated silica helps lift away surface plaque and some surface staining during normal brushing.
If deposits have already hardened into visible tartar, toothpaste and a toothbrush usually cannot remove them completely because tartar is firmly attached to the tooth surface. In that case, a dental cleaning is the appropriate option. After a cleaning, an anti-tartar toothpaste like this can be useful as part of a consistent routine to help slow the build-up that starts from plaque.
For better results, brush thoroughly twice daily and pay attention to areas where deposits commonly appear, such as the inside of the lower front teeth and along the gumline. Interdental cleaning is also important, because toothpaste only works where the brush and foam can reach. If tartar forms quickly despite regular brushing, ask a dentist or hygienist to check your technique and recommend the right cleaning interval.