Solar panel without diodes
Those are 10SQ050 50 V 10A Schottky diodes which are specifically sold as solar panel "anti shading" bypass diodes.   They should not be removed - removing them produces absolutely no change during normal operation but removes a useful function when the panel is shaded. 



From your description it is possible that 2 of the diodes are used in shading bypass mode and one is in series with the panel output. If this is the case then the output would be reduced by an extremely small amount in operation but this would have zero affect on operation in most cases and utterly minimal effect if a high quality MPPT converter was used. These are very good performance diodes - series voltage drop at rated current is lower than most Schottky diodes usually encountered - probably around 0.6V at full current. If the panel is used with a non-MPPT converter this voltage drop will have no affect on the available power. If used with an MPPT converter it would perhaps reduce output by about 1% to 2% in full sun. Other variable losses would swamp this - non solar tracking, dirt on panel, temperature effects etc. 

Without a series diode SOME battery energy will drain through the panel. This will usually be nowhere near as large as full panel current as a non illuminated panel acts as a low current current sink when voltage is applied. Some greater losses may occur during the dawn and dusk periods as panel voltage rises but is below battery voltage. 


They do no harm whatsoever in normal use, do not reduce panel output in any way and allow the panel to produce some output when cells in one of the series strings are shaded. 
In a high voltage system with multiple panels they also provide protection against reverse voltage destructive breakdown if the panel is shaded while the rest of the array is in bright sun. If a cell breaks down in such conditions it is common for a physical hole to be burned in the panel where the shaded cell used to be. [When only a single panel is used the voltages experienced are extremely unlikely to be high enough to cause this effect].


10SQ050 Datasheet here maybe.
And here