Is old I-797 required to travel?

Hi,
Employer A sponsored my H1B visa and I have I-797 document and H1 stamping from employer A. Later Employer B filed cap exempt pitetion for me and have I-797 from employer B.
Now I have I-797 & H1B stamping from employer A and Only I-797 from employer B.

Now I joining and planning to travel for employer B
But employer A, asking me to surrender I-797 document to get release.
H1 stamping from A is valid upto June 2017

Is it OK to surrender I-797 document to employer A?
Is that OK to travel for employer B having I-797 from B and H1 stamping from A?
Will there be any questions at Port of entry asking about original I-797 from A?
Will there be any issues in future by not having the I-797 from A?

Please advise.

Take a copy of 797 and return it to A. A can withdraw their 797 even without having possession of the original doc, but getting it from you may satisfy their ego.

At PoE, they should ask for B’s 797 and not A’s. Still you would have the copy and can let officer know that original was returned to A as part of exit process.