The pact of Umar was between the overthrown Muslims and the conquered non-Muslims. This pact was requested by the Orthodox Christians so that Muslims and non-Muslims know what they can and can not do.
Public Religious Displays
The non-Muslims were not allowed to harbor any spy's in their churches or houses. They were also not allowed to conceal any enemies of the Muslims.
Non-Muslims will receive any Muslim travelers into their homes and give them food and a place to stay for three nights.
Non-Muslims shall not display the cross upon their churches or their sacred books in the streets or in the market-places of the Muslims.
Non-Muslims were not allowed to mimic Muslims by dressing in similar ways. They were not allowed to wear caps, turbans, sandals, or part their hair.
If the non-Muslims were to break their part of the agreement, the Muslims could treat the Christians as enemies and rebel against them.