The reason the adjustment was not pulled, in this situation, was because nothing "financially significant" was changed on the adjustment.  

For the GLI to pick up an adjustment, one of the following needs to be changed from the original:  Credit_Account, Debit_Account, or Fund.  There are also various optional financial adjustment fields that could trigger the GLI picking it up (and would need to be setup on the client's system).  For future reference (or this issue, if you so choose), a list of the Optional Financial Adjustment Fields can be found here, along with where to set them.
 
https://www.blackbaud.com/files/support/guides/ta5/Spctv33/Optional_Financial_Adjustment_Fields_.htm
 
The current options to get the adjusted Transactions pulled by the GLI are:
  1. Adjust one of the core "financially significant" values (Credit_Account, Debit_Account, or Fund), then adjust it back.  That will bring over, to the GLI, both the version with the wrong value, then negate that and bring in the one with the right value.  OR
  2. Set one of the optional financial adjustment fields for something insignificant to their business and do another adjustment to change that.  For example, the field "Office" could be set as "financially significant", then set to some value. That would prompt the GLI to pull the transaction.