Washing the skin of a dead rat

A somewhat crude but memorable equivalent is:

"You can't polish a turd."

It also gives an idea of what the result would be if you could do it.

"Lipstick on a pig."

is a similar expression, but typically used in different situations, where you can do it.

The "polish" idiom is usually said when someone suggests or is about to do something that will be a waste of time. (In design, this would be when someone suggests making improvements to something that is already so fundamentally bad that it should be discarded.)

The "lipstick" idiom is usually said after something has already been improved, made to look more attractive even though what's underneath the makeup remains just as ugly as it ever was. (In marketing, this would when someone repackages the same useless product in order to increase sales.)

A very old saying comes to mind: "you can't make a silk purse out of a sow's ear" meaning it's very difficult to make a fine article out of inadequate material, or it's impossible to train a very stupid person to become the owner of a brilliant mind.

• One cannot turn something inherently inferior into something of value. This proverbial metaphor dates from about 1500, and with some slight variation (“silk” is sometimes “velvet”) makes its way from proverb collections (by Howell, Ray, Dykes, et al.) into literature (Samuel Richardson, Laurence Sterne, Jonathan Swift, Charles Lamb, Robert Browning, George Bernard Shaw, and Clifford Odets, among others). TFD

I would choose Flogging a dead horse

"to waste effort on something when there is no chance of succeeding"

There is a very fine old proverb in English that goes like this:

Though you bray [that is, crush] a fool in a mortar, you may not drive his folly from him.

The image is of using a mortar and pestle to crush something to a fine powder, and the idea is that the fool's folly is inextricable from his being and so cannot be separated from him even with the greatest effort. The saying comes from Proverbs xxvii: 22 in the Old Testament. Bartlett Whiting, Proverbs, Sentences, and Proverbial Phrases from English Writings Mainly Before 1500 (1968) reports instances of this proverb in English sources from circa 900 and 1395. John Bunyan mentions it in "The Aceptable Sacrifice" (1688):

Solomon intimates, that it is a hard thing to make a fool become wise. 'Though thou shouldst bray a fool in a mortar among wheat with a pestle, yet will not his foolishness depart from him,' {Pr. xxvii. 22.}

The proverb also appears in or is alluded to in such works as Samuel Butler's Hudibras (1684), Tobias Smollett's The Adventures of Roderick Random (1748), and William Blake's The Marriage of Heaven and Hell (1793). Nevertheless, it seems to be rarely used today. Bartlett Whiting, Modern Proverbs and Proverbial Sayings (1989), which reports occurrences of proverbs from about 1900 to the early 1980s, lists only one instance of the proverb from the twentieth century—in C.E. Vulliamy, The Polderoy Papers (1943):

Bray a fool in a mortar, says the proverb, and he remains a fool.

Still, it seems to be fairly close in sense to the Indian proverb you cite, and I, for one, would welcome its return to common English usage.