If we're talking about traces of Greek culture in modern India and its recent history, it would be extremely difficult to spot any. But this is not because they aren't there, or because the cultural exchanges of the classical era weren't significant. It's because those identifiably Greek intrusions into South Asian culture became progressively integrated into a specifically South Asian framework, a process I'd say roughly belongs to the 1st-6th centuries CE. South Asian culture has continued to evolve and change since then. What was once visibly Greek derived, inspired, or introduced has long since been adapted further into entirely new and different directions. The encounters with Hellenistic Greek culture absolutely contributed to the particular developments of South Asian art, architecture, etc... along with dozens of other influences. It is just one part of South Asia's cultural DNA.

One of the most frequently talked about Greek influences on South Asia, particularly in the north, is statuary, specifically the influence of Hellenistic styles of sculpture with its exaggerated realism combined with dynamic expression of movement and emotion. The subject matter of statuary likewise, with depictions of Greek deities of greater or lesser kinds, like Herakles as you mentioned. This is a fairly uncontroversial example of Greek cultural exchange with South Asia, I would say. As time goes on you start to find Greek sculptors producing statues and monumental sculpture to fit more South Asian tastes, along with South Asian artisans adopting and reinventing elements from Hellenistic Greek forms. Even during the Gupta period you can see visible traces of this influence, from poses and forms to subject matter and visual symbolism. But even by that period we're talking about traces, with most remaining Greek originated symbolism instead having new and specific meaning to South Asian cultures; post-4th century CE reproductions of Herakles imagery in South Asia, or Atlas to take another common example, are not being produced by Greeks, and thus are not being repeated with the associated significance of the figure in Greek spirituality in mind. It's now over 1500 years since the end of the Gupta hegemony over South Asia, and about 2000 since the Kushan conquest of the last known independent Indo-Greek statelets.

A similar ancient example that involves the Greeks themselves would be the significant Assyrian and Near-Eastern influences on Greek material culture, particularly strong during the height of the Neo-Assyrian Empire in the 8th and 7th centuries BCE. This partially led to mass Greek importation of Near Eastern prestige goods such as ivories, metalworks, jewellrey, and also Greek imitations of motif and design for Near Eastern goods in general. It also led to the prominence of sphinxes, griffons, and lions in Greek art among other mythological creatures. This period is known as the 'Orientalising' period, referring to the profusion of Near Eastern goods and their imitations across this time in Greece. But this was also followed by the adaptation of these elements and styles into Greek preferences and economic realities, and eventually what we call Classical Greek culture, which I would say is traditionally thought of as a distinct and specific 'indigenous' culture.

So yes, Greeks did patronise and spread Buddhism, influence architectural styles in South Asia, and styles of dress, for a time. But at this point it would be disingenuous to point to a hypothetical brooch present on many modern Indian statues to go 'this is really Greek actually because it very distantly originates from the Madeupbroochikon introduced by the Greeks in the 2nd century BC' because the gap between the former and the latter by this point is so wide, and you would need to be familiar with large swathes of Indian and Greek art history to even be tempted to draw a connection.

During their period of power in Bactria and India Greeks heavily influenced South Asia's depictions of the human form, architecture, coinage, and religious practices by the introduction of Greek gods and associated imagery but also by some Greeks becoming major patrons of Buddhism. But cultures move on, and are fully capable of adapting elements of previous prestige cultures into their own to the point of being unrecognizable. I find the cultural interactions of Greeks in Bactria with the existing cultures of the region to be fascinating, but it has to be taken for what it is- a highly influential cultural interaction that led to new cultural directions in South Asia a long time ago, and South Asian cultures have continued to change in the two millenia since. It's not an exciting answer to your question but it is the truthful one.