My HOA is doing this renovation project, which needs to get access and modify the balcony (where I have my screens), and asking me to pay the cost of removing and reinstallation? Do I have the right to request HOA to pay for it? Because this is a HOA project. If not for HOA project, I would not need to remove and reinstall it back. I am in California. In addition, before the project starts, no one came in my unit to inspect it, and I do not see any need for this renovation. Thank you.
It depends on the details of your condo's declaration. It's very common for balconies to be limited common elements, that is, the balcony is actually owned by the condominium as a whole, but you are entitled to exclusive access to it. Depending on the details of the declaration the HOA may be entirely responsible for maintenance of the balcony or the owner may be partially responsible. The declaration may also state whether owners are allowed to make modifications like installing screens.
To figure out whether the HOA needs to pay for the screens you installed you'll have to look at the declaration in detail and probably consult a lawyer.