You do need such letter because

for loan company, they not ony need you to prove you currectly are employed, but also to show your employment history to see if you have a stable job. If you only have current job for a few months, you may not be able to get loan. In addition, you are under H-1B, you definitely need to provide your immigration status to prove that you will not leave the country within next few months or a couple of years. Our law firm eften receive such requests from our alien clients to issue such letter, in addition to your employment letter.