@John ****
Agree. My guess is that the small piece of paper is in fact the receipt you get when you submit a TM-30. This is to be contrasted with a full A4 sheet of paper with a photo when one gets a Certificate of Residence from immigration.
The bank is being flexible in what they will accept for proof of residence. That is a good thing and they are to be commended for that.
The Land Transport Office is not known for being as flexible. You are required to prove your residence by one of the following: yellow house registration book, work permit showing residence, certificate of residence from immigration, affidavit of residence from your passport's embassy. It's rare that they will accept anything else. One can certainly argue that a TM-30 receipt shows your address and is dated and issued by immigration. All that is true, however often the LTO will not accept as proper evidence because that is not listed as acceptable documentation in their operating guidelines.