[quote user="StanH"]

I have IMAP.

 Does this mean that for every email that I store in the Pegasus database, I have to load Gmail into Firefox and delete it there?

Can I delete emails from Gmail within Pegasus?

[/quote]

This question makes me think that a clarification is needed about how IMAP works.  The IMAP protocol, unlike POP3, does not download messages.  It simply allows you to access (mount) a remote mailbox in an email client.  The messages remain on the remote server and only cached locally (optional in Pegasus Mail) unless you manually copy them to a local mailbox folder.  The cache is what allows you to view messages offline.  Configurations in both the email client and the remote server control how deletes made in the client are handled on the server. 

Gmail still supports POP3 so you might consider using it instead of IMAP if you want to download messages to a local mailbox and have them removed from the Gmail mailbox once downloaded.

I am aware that Gmail is set up to not remove messages from their servers. But it is annoying to see them there when I do a word search in Gmail. How can I prevent Gmail searches from detecting messages that I have stored in my local Pegasus mailbox?

depends on whether you use IMAP or POP3. If IMAP, the messages are stored on their servers until you actively delete/expunge them etc.

I have IMAP.

 Does this mean that for every email that I store in the Pegasus database, I have to load Gmail into Firefox and delete it there?

Can I delete emails from Gmail within Pegasus?

[quote user="StanH"]

I have IMAP.

 Can I delete emails from Gmail within Pegasus?

[/quote]

Yes, but you will need to read the relevant documentation on the web interface and set up Gmail the way that you want it to work.