Well, Greek influences still exist in the area in the form of Greco-Buddhist art, like this, and this

Hellenistic influences remained a major part of the cultural and political landscape after the 1st century BCE as evidenced by the Kushan Empire adopting Greek epithets and using the Greek writing system as well as being perpetuators of Greek culture in the area. In addition many Greek communities and cities may have remained at least marginally independent under their own princes due to coinage being issued as late as 150 BCE bearing the names of Greek kings.

During the Roman Republic and Roman Imperial Period trade flourished between Rome and India and was likely conducted primarily by Greek captains and merchants, at least at first. By the fall of the Ptolemaic Kingdom in 30 BCE Hellenistic culture had already permeated the Mediterranean to such an extent that the continued trade between India and Rome brought with it certain cultural ideas and products with Greek origin. The Byzantine Empire had a much larger Greek influence than the Western Roman Empire had, in some ways it resembled Hellenistic culture more than it did the Western Roman Empire, and trade continued between the Byzantine Empire and India well into the 5th century BCE. It was briefly disrupted by the Sassanian conquests but the key territories to Indian trade were retaken during the Byzantine Emperor Heraclius' reconquest in 628. However the Islamic conquest of Egypt which began aroun 639-640 saw a great decline in trade between India and the Mediterranean, and a subsequent increase in trade among South-East Asia which had a much larger cultural impact than Roman trade.

The total effects of Greek influence in India are hard to pin down because interaction between Greece and India began as early as the 4th century BCE with many Indian and Greek traditions having uncertain origins, Sanskrit additionally contains certain Greek loanwords and communities in the Hindu Kush still claim Greek descent today. Another thing that confuses the issue is the fact that many traditional Indian beliefs and practices either emerged or flourished in the Greek period leaving some to attribute Greek origins or at least influences to them. One thing that can be certain is that the ramifications of Hellenization in India, and of India in the Mediterranean, can still be seen today if you look closely.

Sources:

Geographica by Strabo

Geographia Ptolemy I

Natural History by Pliny

Tacitus

Rome by Cassius Dio

The Histories by Polybius