Run the below SQL command in phpMyAdmin. Replace portion CODE_TO_SEARCH with the code you want removed. Make sure database table prefix matches the site you are doing this on.
update wp_posts set post_content = replace(post_content,'Text to find','text to replace with');
ANOTHER WAY BELOW:
phpMyAdmin includes a neat find-and-replace tool.
Select the table, then hit Search > Find and replace
This query took about a minute and successfully replaced several thousand instances of oldurl.ext
with the newurl.ext
within Column post_content