meaning - what do "for a time" and "backtrack" mean in this specific sentence

In a paper of Scientific American, there is a sentence as follows

Einstein understood early on that they [the gravitational waves] were implied by his theory but for a time backtracked from his original, correct claims for their existence.

I understand the first sentence: "Einstein understood early on that they [the black holes] were implied by his theory", and I think the meaning of the rest should be "but for a time, they were backtracked from his original, correct claims for their existence".

However, I don't understand the meaning of the phrase "but for a time" and "backtrack", therefore I can't understand the whole sentence.

Please explain to me.

English is not my native language, so I beg your pardons for my poor one.

Thanks.