Beatles songs written by women?

Three female songwriters have co-credits on songs covered by The Beatles

Carole King for Chains (music), Georgia Dobbins (words and music) and Janie Bradford for Money (words).

What do these songs have in common?

They were all American and all minor hits on the US charts in the years leading up to The Beatles first recording contract. They were widely known amongst the band's peers but not to wider UK record buying market. 

The Beatles would gave shout outs to the artists who made the original recordings - "this is a Marvellette's number' - but not usually to the songwriters.  Their credits only appeared in tiny writing on the physical singles -  often in combinations of unfamiliar surnames.

Of course they were aware that the songwriters received royalties - this drove the Lennon & McCartney partnership from their teen years. But songwriters would not generally become household names until their own success. 

Carol King was familiar to them as Goffin & King were perhaps the famous songwriting team in the Brill Building. But The Beatles never made public reference to Bradford or Dobbins, presumably assuming that they were 'backroom boys'.

Feminine sensibility?

The Beatles were not prototype feminists but they were musically open minded. They were more interested in the sound of the 'go 

Chains and Please Mr Postman are clearly sung from a feminine perspective. Here’s Marvelettes, Georgia Dobbins on her contribution to Please, Mr Postman:

I was waiting for the postman to bring me a letter from this guy who was in the Navy. That’s how I came up with the lyrics. Then I made up the tune. I just hummed it over and over and changed it to the way it should be. I improvised.

Money is more ambiguous. Tough generally performed by male acts the point of view is in the same tradition as Diamonds are a Girl's Best Friend 

Very much the Lennon and McCartney approach.