If a stock is demoted from a Guru Screen, does that mean it's a sell?

Firstly, it's important to reiterate that the Guru Screens are not simply Buy Lists - in investing, it's always important to Do Your Own Research (DYOR), whether that be stock-specific research to understand the underlying fundamentals if you are a 'Hunter' or screen-specific research to understand the underlying criteria if you are a 'Farmer' (here's what we mean by that Hunter vs. Farmer distinction).

Secondly, it's important to appreciate the distinction between the list of qualifying stocks - which can change every day - and our tracked portfolio (which only changes quarterly - this generates the performance chart). While the qualifying lists of stocks for each screen updates daily [based on price movements and fundamental changes, we track all the Guru Models as baskets and we update or 'rebalance' the basket every three months (i.e. we mechanically sell or hold the current basket based on whether they are still qualifying at the quarter end).
A key part of the DYOR aspect of using the Guru Screens is to decide on appropriate sell / rebalancing rules and timeframe that suits your investing style. In our own tracking of the models, we use a three month mechanical rebalancing but this will not be suitable for all investors. Aside from a strict mechanical approach to selling, there are many other selling strategies.

The reason that deciding on the right rebalancing period is so important is because, to always sell a stock as soon as it no longer qualifies under the original mechanical buying criteria could lead to massive over-trading. Some Guru Screens, especially the momentum ones, can be highly volatile depending on market conditions - with stocks appearing and disappearing from the lists almost daily, so the frictional costs of implementing the strategy this way would skyrocket, likely overwhelming any outperformance.

Unless you are a momentum trader or an institutional investor with massive scale, it's unlikely to be optimal to have a rebalancing period that is much shorter than three months. Typically, a private investor would rebalance annually or semi-annually.