If you already have the paid CSS upgrade you can add:
to your stylesheet and it will remove the picture of the quote marks. If you don’t have the CSS upgrade you’ll have to rely on inline styles which will work for now, but there is/was talk of removing this feature, so it might not work forever.
Instead of using the <blockgquote> tag when writing your post, switch to the HTML editor and add your inline styles to a regular paragraph tag. To get it to look the same as before but without the image place your text between tags like the ones below.
<p style="border:1px dashed #CCCCCC;margin:5px 0;padding:8px 12px 8px 36px; background-color:#F4F5F7;">
TEXT GOES HERE