You want to check and uncheck use boolean values in prop, do not use removeProp
which may end up removing the checked property from the element in some browser as you mentioned and can cause issues like this.
function check() {
$("#box").prop("checked", true);
}
function uncheck() {
$("#box").prop("checked", false);
}
See doc
The .removeProp() method removes properties set by the .prop() method.
With some built-in properties of a DOM element or window object, browsers may generate an error if an attempt is made to remove the property. jQuery first assigns the value undefined to the property and ignores any error the browser generates. In general, it is only necessary to remove custom properties that have been set on an object, and not built-in (native) properties.
Note: Do not use this method to remove native properties such as checked, disabled, or selected. This will remove the property completely and, once removed, cannot be added again to element. Use .prop() to set these properties to false instead.