You cannot remove the jobs that you have applied for in Driver Pulse. This is primarily so that you can remember to which companies you have previously applied. This is private information that only you have access to; carriers are unable to see this data.
If you would like to make sure that carriers cannot contact you, you have the option of blocking a carrier in Driver Pulse. For steps on how to do that, please see the following article: How do I delete or block a carrier in Driver Pulse?