As for the American band that's making a cover of the song, and collecting money - isn't there enough dirt in their own country to sing about... ?! If not, I could tell them lol. That's kind of the whole point of punk. Local people, local issues. Their action is exactly what the establishment in their own country wants them to do. Doh!
If anyone should make a cover, it should be another Russian band, of course! Otherwise it is pointless.

However in order for them to sing the song, they had to translate it to English first. Here is their translation:

Lyrics to Punk-Prayer "Virgin Mary, Put Putin Away" by PUSSY RIOT
Lyrics via Lyrics of Songs of Pussy Riot | Free Pussy Riot!

(choir)

Virgin Mary, Mother of God, put Putin away
Рut Putin away, put Putin away

(end chorus)

...
Black robe, golden epaulettes
All parishioners crawl to bow
The phantom of liberty is in heaven
Gay-pride sent to Siberia in chains

The head of the KGB, their chief saint,
Leads protesters to prison under escort
In order not to offend His Holiness
Women must give birth and love

Shit, shit, the Lord's shit!
Shit, shit, the Lord's shit!

(Chorus)

Virgin Mary, Mother of God, become a feminist
Become a feminist, become a feminist

(end chorus)

The Church’s praise of rotten dictators
The cross-bearer procession of black limousines
A teacher-preacher will meet you at school
Go to class - bring him money!

Patriarch Gundyaev believes in Putin
Bitch, better believe in God instead
The belt of the Virgin can’t replace mass-meetings
Mary, Mother of God, is with us in protest!

(Chorus)

Virgin Mary, Mother of God, put Putin away
Рut Putin away, put Putin away

(end chorus)