Workaround 1;

input[type=text]::-ms-clear {
    display: none;
}

Workaround 2: 

// https://www.telerik.com/support/kb/aspnet-ajax/details/how-to-create-a-javascript-array-of-all-particular-radcontrols-on-the-page
function get_allRadDropDownTrees() {
    var allRadDropDownTrees = [];
    var allRadControls = $telerik.radControls;

    for (var i = 0; i < allRadControls.length; i++) {
        var element = allRadControls[i];

        if (Telerik.Web.UI.RadDropDownTree && element instanceof Telerik.Web.UI.RadDropDownTree) {
            Array.add(allRadDropDownTrees, element);
        }
    }
    return allRadDropDownTrees;
}


function fixClearButton(sender, args) {
    tree = sender;
    if ($telerik.isIE) {
        var dropDownTrees = get_allRadDropDownTrees();
        dropDownTrees.forEach(function (dropdowntree) {                       
            $telerik.$(dropdowntree.get_filterElement()).on('input', function (e, a) {
                if (!e.target.value) {
                    dropdowntree.filterByText("")
                }
            })
        })
    }
    Sys.Application.remove_load(fixClearButton);
}

Sys.Application.add_load(fixClearButton);



Workaround 3: 

var tree;
function OnClientLoad(sender, args) {
    tree = sender;
    if ($telerik.isIE) {
        $telerik.$(sender.get_filterElement()).on('input', function (e, a) {
            if (!e.target.value) {
                tree.filterByText("")
            }
        })
    }
}