If you are still an eligible individual, you can apply the remining $300 as part of your 2025 HSA contribution. Doing so avoids the double taxation and 20% additional tax on the $300 and eliminates the 6% excess-contribution penalty for 2025. Otherwise, to eliminate the penalty for 2025 you would have to take an ordinary distribution from the HSA and make it taxable by not applying it to medical expenses.
"Do I need to issue some special request to my employer or the company managing my HSA?"
The only thing that you might need to do is, if you are an eligible individual for 2025 and HSA contributions are being taken from your pay, make sure that your HSA contributions via your employer are not so much that you would not be able to apply the $300 as part of your 2025 contribution. If you will be an eligible individual all of 2025 and new contributions for 2025 will be similar to those in 2024, it seems that you are already set up to have the space to apply the $300 to 2025.
