This is my code.
I run the project and all is well.
I clear the Checkbox and the column groups disappeared and not restored even when I change again the column visibility.

<Window x:Class="TestTelerikGridViewDesign.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:telerik="http://schemas.telerik.com/2008/xaml/presentation" 
        xmlns:local="clr-namespace:TestTelerikGridViewDesign"
        mc:Ignorable="d"
        Title="MainWindow" Height="350" Width="625">
    <Grid>
        <Grid.RowDefinitions>
            <RowDefinition Height="Auto" ></RowDefinition>
            <RowDefinition Height="*" ></RowDefinition>
        </Grid.RowDefinitions>

        <CheckBox Margin="6" Name="ShowColumnsSelector" IsChecked="True" ></CheckBox>
        
        <telerik:RadGridView Grid.Row="1">
            <telerik:RadGridView.ColumnGroups>
                <telerik:GridViewColumnGroup Name="Group1" Header="Group1" ></telerik:GridViewColumnGroup>
                <telerik:GridViewColumnGroup Name="Group2" Header="Group2" ></telerik:GridViewColumnGroup>
            </telerik:RadGridView.ColumnGroups>
            <telerik:RadGridView.Columns>
                <telerik:GridViewDataColumn Header="Col 1" ColumnGroupName="Group1" IsVisible="{Binding ElementName=ShowColumnsSelector,Path=IsChecked}"/>
                <telerik:GridViewDataColumn Header="Col 2" ColumnGroupName="Group1" IsVisible="{Binding ElementName=ShowColumnsSelector,Path=IsChecked}"/>
                <telerik:GridViewDataColumn Header="Col 3" ColumnGroupName="Group2" IsVisible="{Binding ElementName=ShowColumnsSelector,Path=IsChecked}"/>
                <telerik:GridViewDataColumn Header="Col 4" ColumnGroupName="Group2" IsVisible="{Binding ElementName=ShowColumnsSelector,Path=IsChecked}"/>
            </telerik:RadGridView.Columns>
        </telerik:RadGridView>
    </Grid>
</Window>

deleted by yealter