?? if all you want is the RSS (the orange icon) why did you put in your own email icon?
But no matter - since you put in the HTML, you can pull out what ever part you don't want...or use CSS to hide it. your code looks like this (the lines of ='s are just for illustration purpose) lso, I formated the code for ease of viewing
HTML Code:
<div id="bfa_subscribe" class="widget widget_bfa_subscribe">
<form class="feedburner-email-form" action="http://feedburner.google.com/fb/a/mailverify" method="post" target="popupwindow" onsubmit="window.open('http://feedburner.google.com/fb/a/mailverify?uri=GoneScamping', 'popupwindow', 'scrollbars=yes,width=550,height=520');return true">
<table class="subscribe" cellpadding="0" cellspacing="0" border="0">
===========================
<tr>
<td class="email-text" colspan="2"><p>
<a href="http://feedburner.google.com/fb/a/mailverify?uri=GoneScamping&loc=en_US">
<img src="http://www.gonescamping.com/wp-content/themes/atahualpa353/images/feedburner-email.gif" style="float:left; margin: 0 7px 3px 0" alt="" /></a><a href="http://feedburner.google.com/fb/a/mailverify?uri=GoneScamping&loc=en_US">Subscribe to Gone Scamping by Email</a></p>
</td>
</tr>
===========================
<tr>
<td class="email-field">
<input type="text" name="email" class="text inputblur" value="" onfocus="this.value='';" />
<input type="hidden" value="GoneScamping" name="uri"/>
<input type="hidden" name="loc" value="en_US"/>
</td>
<td class="email-button">
<input type="submit" class="button" value="" />
</td>
</tr>
============================
<tr>
<td class="post-text" colspan="2"><p>
<a href="http://www.gonescamping.com/feed/">
<img src="http://www.gonescamping.com/wp-content/themes/atahualpa353/images/post-feed.gif" style="float:left; margin: 0 7px 3px 0" alt="" /></a>Subscribe to posts in a reader</p>
</td>
</tr>
===========================
<tr>
<td class="comment-text" colspan="2"><p>
<a href="http://www.gonescamping.com/comments/feed/">
<img src="http://www.gonescamping.com/wp-content/themes/atahualpa353/images/comment-feed.gif" style="float:left; margin: 0 7px 3px 0" alt="" /></a>Subscribe to comments in a reader</p>
</td>
</tr>
===========================
</table>
</form>
</div>
you have a <div..> with a <form..> inside it that has a <table...> with four rows. These four rows are the rows you see on the page (well three since you hid one with CSS ...umm on a side note are you editing css.php?? you shouldn't, just go to ATO->Add HTML/CSS Inserts->CSS Inserts and add it there. this will then make it a theme option and you don't have to worry about updating the code during the next upgrade.)
You can remove the row (<tr>...</tr> for which ever rows you don't want, or you could use CSS to hide them. For example, to hide the last row, you create the CSS Selector from the column class 'comment-text' and add the rule 'display:none; to get
HTML Code:
td.comment-text {display: none;}
You know, if all you wanted was the first one, you could just have used a text widget and put the HTML for that in the widget and skipped using the BFA_Subscribe widget altogether.