I called recon and the rep said that the mortgate inquires by the lenders were not reported as mortgage in EQ and they cannot approve it now. They suggested to contact EQ to correct the inquiries and afterward, call them again.
I checked CK and the mortgage inquiries in both EQ/TU were not reported under any category ("Miscellaneous Reptg. Agencies"). Only EX reported them correctly. I guess it is the issue of EQ/TU but not the lenders.
It looks weird. I will call EQ, not sure whether it is straightforward to correct these inquiries over the phone. Is there any suggestion?
Anyway, it looks like after corrections, one more HP is needed 
. It was good if they could pull EX instead of EQ.
Fico8: EX~EQ~TU~840 (12 month goal~850).It looks like the disputes should be submitted by the link below and it will take ~30 days for EQ to fix any issue:
https://www.equifax.com/personal/credit-report-services/credit-dispute
The recon letter mentions a 60 day period to call. Anyway, if it needs HP again, it can be a new application submission and it does not need to meet the 60 day period.
I submitted disputes to EQ. It takes ~30 days to respond but at the end, Citi possibly needs one HP again to check the results (I do not have any credit card with Citi). If it is SP it is ok, but for HP, I am not sure whether it is the best card for Costco purchases.
In general, I think, the best matching cards for costco purchases are coming from BOA but not Citi. BOA Cash Rewards card gives 3% cash-back and you can use it for online shopping at Costco or any other shop (pick-up in store). I have two BOA cash rewards already and I can use this HP to get the third one 
, instead of Costco card.
Citi looks a bit strage bank. After fixing the mortage inquiries in the EQ report, I called recon again. Now they tell me that the reason for "too many inquiries" that resulted denial was not the mortage inquiries but it was due to one HP from another bank on the same day that I applied for the Citi Costco card and it raised a flag (I applied for Chase CSP and approved on the same day). Did anybody saw this issue to get denied because of applying for more than one card on the same day?
In the past year, I applied for only two CCs (Chase CSP and Citi Costco). The rep was recommending that if I want the card, it is better that I wait for several months to drop off the inquiries from my EQ report and apply again. The rep said that if I want to proceed to this application now, another HP is needed but it is less likely that it can get approved. Not sure whether such denial reasons exist in another banks. I could get credit card from several banks but Citi at any time in the past 5-6 years provides one strange reason to deny my applications
Next time and if I want to apply for ~2 cards on the same day or week, it might be better that I place Citi application in priority and afterard, apply for the next card. Previously, I was assuming that Chase 5/24 is the most restricted criteria to approve for a CC (Fico8>770) until receiving such denial reasons from Citi.
Today, the rep was saying that the reason for denial was one HP from the other bank in the same day that that I applied for this Citi Costco. I told her that the provided reason in the letter was "too many recent inquiries" and she said that one HP can be also too many 
. I think the rep was not knowledgable and she wanted to provide any illogical explanation or reason to avoid chaning the denial decision (which I assume was initially taken by algo).
While I am frunstrated from Citi to deny all my CC applications in the past for strange reasons, the denial of the last application is completely illogical (Fico8>780, 2/24). I do not want to burn Citi, to be able to get CC or loan in future, but if somebody thinks that this illogical denial can qualify for complaint submission, I may proceed to it. Anyway, I barely need Costco CC, because the other Visa cards can provide better cashback at Costco. I also have EV and cannot use its 4% cashback benefit on gas.
If you read some of the Citi Custom Cash threads you will see there are DPs on people being denied by Citi when they have 2 inquiries within 5 days.
@Anonymous: The inquiries have category. I am checking EX and almost all inquiries are categorized correctly (CC, mortgate, auto). EQ looks super messy. For mortgage, there is a ~3 week period to apply to multiple lenders and all HPs will get counted as one HP, for Fico8 score calculation. It is illogical to get denied from CC because of multiple HPs for mortgage or autoloan while having Fico8>770.
I guess, Chase got approved my CC because they used EX (all HPs were categorized). But Citi used the super messy EQ and due to multiple mortgate HPs in the past month and one HP on the same day, their algo decided to deny. Not sure about any reasons that the rep was providing today and not sure whether applying in branch could change anything.
Anyway, Citi is down for me for at least one year to drop off all mortgate HPs.