Single messages are built in, bulk needs a helper. Both below.

One message: open it, File, Save As, set Save as type to Text Only (*.txt) and save. The file starts with the From, Sent, To and Subject block, then the body stripped of formatting. Attachments are listed by name in the header block but not saved, export those separately if the ticket needs them.

A folder of messages: Outlook's Save As only handles the open message, so bulk means either a small VBA macro looping the folder and calling SaveAs with the olTXT format or a converter. A PST converter with TXT output, SysTools PST Converter is one, takes the exported folder and writes one .txt per message with the same header block, which keeps the ticketing system's parser happy since the format matches the native Save As output.

Watch the encoding on non English mail either way. The Text Only save uses your system codepage, so if tickets arrive with mangled characters, the fix is switching the system locale to UTF-8 or having the converter output UTF-8 directly.