I've created an ArcGIS tool using ModelBuilder, 10.3.1. One of the inputs must be a numeric value typed in by the user. Thus there is no need for the model to display the default folder selection button for that input (see the red X in the attached screen shot). How do I remove the button so that the user is not tempted to click it?
Model builder parameters have a Type and depending on that type the display and behavior on the tool interface is set.. for example if you set the parameter as 'Feature Class' the browser will only browse for feature classes, either shapefile or geodatabase and not allow numbers, files, folders or drives as input.
You're getting the folder browser because your parameter is set to a type that can be browsed for. Depending on how you create the parameter it is possible to specify the type for variables (right click on blank space, select create variable) but not so much for tool parameters (right click on an oval, select Model Parameter) as the tools themselves have determined the type they expect.
There are limits on how much you can change a variables' type, once created, for a radical change like folder to integer it might be better to remove the parameter and recreate it with the correct type... of course you can change the type to 'any value' but this could cause problems later if you're expecting a number and get a string instead.
For more information read A quick tutorial on creating a model with parameters.