How to stop a trigger of managed package from failing as it is being envoked by Salesforce Batch Apex?

We can't restrict/deactivate manage package trigger untill it is not operated with some condition like we have custom setting checkbox checked to initiate the trigger. If you want to still update the accounts, you have to use the Salesforce APIs to update accounts OR you can make custom webservice in Salesforce and call it by authenticating salesforce. By that way the context would get change of both transactions. Let me know if you need more detail.