If you uncheck the "Public Access" checkbox for the module property in studio, it will not be visible/settable at deployment time in TEA.
Please note that unchecking the public access checkbox would not have any impact on the generated default.substvar file. The value would still be false(<deploymentSettable>false</deploymentSettable>). The values in the profile file do not matter, You should look at module.bwm file under META-INF folder. Here is an extract from the file with one public & one private module property
<sca:property xmi:id="_rh2a4EiKEeSTfvLt9h2MXQ" name="Input_File" type="XMLSchema:string" scalable="true"/>
<sca:property xmi:id="_uR7V0EiKEeSTfvLt9h2MXQ" name="Output_File_1" type="XMLSchema:string" publicAccess="true" scalable="true"/>
This file is being used at deployment to display the property for editing in TEA if it is public