Looks like you haven't set the proxy server.
Might be worth double checking the set up against this.
On the Gigaset:
Go to Telephony/Connections and check the active box for line IP1 and then click edit.
Now change the connection name to the extension number. The authentication name, username and display name all also need to be the extension number.
Set the password to match what was set on the Mitel.
Click on show advanced settings.
The domain and proxy server need to be set to the IP address of the Mitel. The ports need to be 5060 for SIP.
Outbound Proxy should be set to Always.
Optional:
Go to settings/telephony/advanced voip
Enable both ‘Use the R key to transfer’ and ‘Transfer by On-Hook’
Also ensure that Hold on transfer target is unticked for both attended and unattended transfer.
On the Mitel:
Check the SIP Device Capability that are assigned to your extension.
To find out this go to Users & Devices / User and Service Configuration, The extension number, Service Detail.
To modify the Sip Device Capabilities go to System Properties / Feature Settings / SIP device capabilities and locate the associated number.
Enable the following:
Replace System based with Device based In-Call Features,
Prevent the Use of IP Address 0.0.0.0 in SDP Messages,
Suppress Use of SDP Inactive Media Streams
Allow Display Update
Use P-Asserted Identity Header