Hi Ravi,
The Finesse Agent Desktop should be showing the "End" button as soon as the agent is able to end the call. So the fact that the button doesn't appear when the call is dialing the customer, it most likely means this is not possible to perform this action.
You can verify this by looking at the Finesse webservices logs and seeing the Finesse dialog notifications during this scenario. For the agent's extension (mediaAddress), see if the action DROP is part of their list during that moment of time.
<participants>
<Participant>
<actions>
<action>UPDATE_CALL_DATA</action>
<action>DROP</action>
</actions>
<mediaAddress>6002</mediaAddress>
<mediaAddressType>AGENT_DEVICE</mediaAddressType>
<startTime>2017-12-22T18:47:52.070Z</startTime>
<state>INITIATING</state>
<stateCause></stateCause>
<stateChangeTime>2017-12-22T18:47:52.070Z</stateChangeTime>
</Participant>
</participants>
Thanx,
Denise