I understand not knowing what to do and it's stressful. Sometimes teachers are really helpful - will have great suggestions - but where she says that he could use more help - what about a tutor? That was my first thought.
I had to do a lot of work with my kids in the early years of school, especially kindergarten. Do you work with him at home? There are workbooks available (you could ask your teacher for websites on where to order them). I had to teach my kids to read pretty much myself.
My personal thought is that you should be able to catch him up from now till he starts the next grade. You have the whole summer.
A lot of parents (myself included when my first went to school) think that kids are taught everything in school, and that's where they do all their learning. My older sister told me to get involved right from the get go. So my kids went from average to doing really well. Not judging you - but you haven't mentioned what you are doing at home - so that would be helpful. Not all parents know there are resources out there for you.
For example, I just assumed they would teach printing - as they did with my older bunch. No where near the time spent on this at school any more. So one of mine had real difficulty. I was just told that they were struggling, and offered no help by the school. So I tried to help - but it wasn't until I arranged for my child to see an OT specialist - and we got the help we needed - privately. I got the printing work books, I spent 10 minutes a day - every day - until now my little one is caught up - not to everyone else, but at least it's not holding her back.
I'm not a fan of holding kids back in general if it's just one thing they are struggling with - but I've read on this site so many moms who said their children benefited from doing a year over or waiting to start school. Usually it's because of where they are socially or maturity wise, or they are super young for the class year.
Is there someone else you can reach out to at the school - to get a second opinion? What about a school psychologist or counselor? I think I'd try that.
Good luck :) Keep us posted
ETA: Read your SWH.
Couple of suggestions. We worked with an OT specialist (fun lady who made learning fun) for motor skills with my youngest. She too held pencil in a fist. Really helped.
Second - has your son been tested for Dyslexia just to rule that out? Likely doesn't (kids' reading comes along at such different paces in the early years) but good to know.
My mom taught kindergarten for 30+ years - typical and special needs kids. She had enough experience to give parents her honest opinion and could suggest things that worked for families in the past. Sounds like you need this type of guidance. If your teacher isn't that experienced - then definitely look for someone in the school. It's not to discredit your teacher - just say you're confused and would appreciate more input.