How to specify character style to anchored objects markers depending on the objects formats?

Question

I have a long document contains much of anchored text frames with custom positions and want to delete them by aplying character styles to their markers.

Answer 1

Create a new character style to apply it. And change the character style name in this code to yours, then execute it.
main ();
function main (){
    app.findGrepPreferences = NothingEnum.NOTHING;
    app.findGrepPreferences.findWhat = "~a";
    var objectsArray = app.activeDocument.findGrep();
    for (var c = 0; c < objectsArray.length; c++) {
        if (objectsArray[c].textFrames.length > 0) //The anchored object is a text frame
            var targetTextFrame = objectsArray[c].textFrames.item(0);
            var textFramePosition = targetTextFrame.anchoredObjectSettings.anchoredPosition;
            if (textFramePosition == AnchorPosition.ANCHORED) // the object have custom position
                //Create a new charater style and change the character style name to yours. 
                objectsArray[c].appliedCharacterStyle = app.activeDocument.characterStyles.itemByName("Delete");
Then make a GREP search for this character style, and if you want delete them all by Change All button.