You don't ever need to strain them but fresh green beans tend to be a bit stringy and don't puree super smooth. I'd imagine frozen don't have the same gritty texture so you're probably just fine. And even if they are, it's not the end of the world. I used fresh and never strained them and my son still ate them at 5 months with no problems. It's more of a textural thing.
Warning
No formatter is installed for the format bbhtml
I didn't strain ours and DD ate them....although, it did take her 2-3 times of eating them to get used to the texture. They weren't smooth like the sweet potato and squashes were. But, she eats them without a problem!
Warning
No formatter is installed for the format bbhtml
Re: DIY pureed frozen green beans question