Salesforce does support installing managed packages into Group Edition orgs, however, your managed package cannot be dependent on features that are not supported in Group Edition orgs — such as Record Types, Custom Report Types, Force.com Sites, and a laundry list of other features.

So it sounds like your package includes one or more Custom Report Types you created, but Custom Report Types are not a supported feature in Group Edition. Therefore you will not be able to install your package into any Group Edition org until your package no longer includes Custom Report Types. 

However, I do not think that at this time it is possible to remove Custom Report Types from a managed package once the Custom Report Type has been included in a “Managed - Released” version.

If the Custom Report Type was included in a Managed - Released version, rather than a Managed - Beta version, you may want to contact Salesforce.com Support and see if they can revert this package to a Managed - Beta, at which point you could remove the Custom Report Types and any other components that will not work with Group Edition. They may or may not be able to support this request. If they are not, you may have to move your code to a new dev org, and start over again, in order to have your app work with Group Edition — but for your sake let’s hope you don’t have to go through that.

I found Zach again on my quest for GE to install a managed package from AppExchange but I’m not sure how to decapricate the call for the record type: custom reports.

http://salesforce.stackexchange.com/questions/547/building-an-app-that-works-in-group-professional-edition?rq=1

Help!

Here is the documentation on what components you are able to delete from Managed - Released packages:

http://docs.releasenotes.salesforce.com/en-us/spring14/release-notes/rn_forcecom_isvforce_managed_co…

Thanks Zach.  Spot on.  I had to do the Beta rollback before for another app and its a total nightmare.  If I find another way around my issue I will post it here.

I found another way around:

Flexible Managed Packages (Generally Available in Spring’14 Release)If you are a salesforce partner that builds your offerings on Force.com platform using managed packages functionality, you are painfully aware of the limitations in terms of modifying or removing components after uploading the “managed-released” version of your managed package. (Please refer to the ISVforce Guide for a component-by-component description of manage-ability and edit-ability.) With the Spring’14 release, we are relaxing this restriction for a few component types. With Spring’14, if we enable this feature for your managed package, you can remove the following component types:
1. Custom Tabs
2. Custom Fields
3. Record Types
4. Validation Rules
5. Field Sets
6. Custom Buttons & Links
7. Custom Objects (with some restrictions; see documentation)
As you can expect, you can do so only if the component has no references. For example you cannot remove a custom field if it is referenced in a validation rule. You have to modify the validation rule and remove the reference to the custom field before you can delete the custom field. Please refer to the ISVforce Guide for a full list of restrictions.
Once you delete a component it is only removed from your package. Future package installations will not contain this component. When an existing customer upgrades to the version where you have removed components no data or metadata is ever deleted in their organization without specific action by the customer. Subscribers who upgrade to the new package version will still have the deleted components available in their organization. It is up to the customer org sys admin to understand the implications of deleting these components from their org and choose to delete them. Please refer to the release notes for more details. Search for Deleting Components in a Managed Package in Spring’14 release notes.
Deleting components is a destructive operation. You CANNOT undo the delete operation, even if you make a mistake. For example if you delete a custom field and try to create a new custom field with the same name, you cannot re-use the same API name.
We strongly recommend that you fully understand this feature, read the documentation, and optionally test out this feature in a test packaging org before removing components from your official packaging org. Also, analyze and understand dependencies of the components with your extension packages, if any, before removing them.

Thanks Zach