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YMMV, but I asked my bank not to pull ChexSystems when I opened a CD, and they figured out a way. Obviously that doesn't help you with your existing pulls.
If you like this bank's CDs otherwise, it can't hurt to ask. (But maybe you already have.)
@kremonis I pulled my Chex Systems report earlier this week. I have five inquires total by four different banks and a credit unions. One bank on the report report I have done business with for several decades. I opened a checking the first new account I have opened with them in a long time. The credit union that I have an account with I opened a second account on line. I thought I had done everything corrrctly in the app to ID myself as an existing member maybe not. From the email(s) I received from the CU thought I was a new member. They figured that out I was existing member and I supplied additional documentation just in case. All went well new the account was opened. The banks and credit unions have laws and regulations that they must follow which includes doing their due dilligence which may include pulling a Chex System report. Some of these laws are a result of things that have happened in the past. The laws and regulations are their to protect the banking systems as well as the consumer.