How do I set permissions that prevent colleagues from being able to delete results?

@EvansAbove When you collaborate the project, make sure to uncheck at least “Edit Survey Responses”: 

Edit Survey Responses: Disabling this permission stops your collaborator from deleting data or using the response editing feature. Also, while you can still generate a retake survey as new response link, you cannot generate a regular retake link. This permission, when disabled, allows collaborators to add data, but not modify existing data in any way.

But you should probably also remove the whole edit/distribute permissions if they should just see response data. 

Please check all the permissions in detail and try with a minimum. 

If you refer to the user permissions in general, please refer to this overview At least “Edit Survey Responses” in the survey permissions section must be unchecked.

Edit Survey Responses: User can edit survey responses in the Data & Analysis tab. When disabled, Response Editing will no longer be an option in the Data & Analysis tab and you will be unable to assign values to Manual Variables. Additionally, users with this permission disabled will not be able to delete responses. This permission also grants access to Text iQ if your brand has access to it.

Best
Christian