If they go to their Donations page after logging into the church web site, there is a settings link towards the bottom of the left side menu. When they click that link, they will see their name, MRN, Address, Stake and Ward (and other information, including the bank account they have set up). If the clerk provides them with an Individual Ordinance Summary from LCR, they can verify if the MRN on their Donations page matches.
Also, further down that page, they can check a box to allow their spouse to see their donations. If they haven't done that and are using the spouses MRN by mistake, that is the most likely cause they are not seeing their donations as russellhltn noted.
If they have been donating to the wrong MRN, I think the clerk can fix it in LCR but each donation will have to be corrected individually.