Let me try to provide better responses to your questions and/or clarify what I meant.
1 - The $500 was a benefit from the employer and was the only HSA contribution they were going to make during the year of coverage under the new HDHP plan. Any other HSA contributions by payroll deduction were by employee choice. So, what I meant below was this this was their contribution to the HSA for the year of HDHP coverage.
2 - She believes coverage under the HDHP plan began Dec 1st 2021 and I agree with your assumption that the employer contributed to the HSA in December based on this start date, as well.
By "cost" in reference to December 2021 per the last-month rule, I meant the additional tax and/or penalty that TT is calculating for an excess contribution in December 2021 for one month HDHP coverage in 2021. Also, I meant that the $500 from the employer was the HSA contribution / benefit for the entire upcoming coverage year under the HDHP which extended into 2022 (not just Dec 2021)
I'm a little confused now on what I should choose to enter in TT for 2022 and what the resulting taxes/penalties will be both for 2022 and 2021 (Dec).
If I select "NO" as you've indicated regarding withdrawing excess contributions, won't this result in the 6% penalty?
For 2021, TT is saying $200 of the $500 is considered "income" for the last-month rule. I assume this is because the entire contribution was made by the employer in December even though HDHP didn't begin until December and then because her coverage under an HDHP ended in April when she switched employers (so she wasn't under an HDHP for all of 2022). Is it correct that she is being 'penalized' in this way because of the timing of the contribution and I should just leave all inputs in TT as they are?
Thank you!
"If I select "NO" as you've indicated regarding withdrawing excess contributions, won't this result in the 6% penalty?"
Yes, but as I pointed out above, the carryover penalty is 6% of the SMALLER of the carryover or the amount in the HSA at the end of the year, Since the amount in her HSA at the end of the year (I assume) was zero, 6% of zero is zero...so no penalty.
"Is it correct that she is being 'penalized' in this way because of the timing of the contribution and I should just leave all inputs in TT as they are?"
The effect of the last-month rule is to allow you the full annual HSA contribution limit, no matter how few months you had the HDHP insurance. So her employer could have contributed $500 (as it did) or $1,000 or the maximum of $3,600, all in December.
The "only" problem with the last-month rule is that you (well, your daughter) has to stay under HDHP coverage for the next year. If she does not (as she did not), then TurboTax has to ask you a lot of questions (which I guess you have seen) to recalculate what the annual HSA limit would have been if there were no last-month rule, and then use that to figure the amount of the excess HSA contribution.
In this case, she would have been allowed for one month an annual HSA contribution of $300 (1/12 times $3,600), so the $500 contribution would have been a $300 HSA contribution and a $200 excess contribution (which, yes, you add to income and pay tax on).
So, because I am not sure what you have entered, I would say, leave everything as it is but make sure that you don't tell TurboTax that you will withdraw the excess contribution for 2022 by April 18th, because you can't withdraw money that isn't there.
So, yes, she will pay tax for "failure to maintain HDHP coverage" - see line 18 on form 8889, but she should not pay a penalty for the carryover of the excess to 2023 - see line 49 on form 5329.
