Can I travel immediately back to India after entering US on H1B in January

USA H1B Visa
1

I came into US in this January on H1B in NewJersey through a consultancy. Now I have got a client in Columbus Ohio and I have moved there. I would want to bring my family to US from India and I need to travel back in March beginning for four days to assist them (since i have a small kid). My company currently tells me that it is of great risk that I am travelling right away back to India (since I arrived this January) and customs would red flag my profile.

1. Is this true? Would I have any more difficulties at the POE when I arrive back?

 

2. My client in Columbus might not give me a client letter. What else can I do to ease my arrival back in US?
2

  1. No. There are no travel restrictions on H1. However U must give an appropriate reason for travel if asked at POE

    1. There might be a chance of asking Client Letter, may be this is the reason employer is not allowing to go back

    Is 1B amendment done for U, as there was a change in location??