I think TSDS was still fitted on llex.
The starboard broadside photo from Maritimequest is of too poor a quality to say whether or not it is fitted at that time. That photo would date to late-May/June/July 1940 before the Med Fleet started to paint to improvised camouflage designs at Alexandria from 5th August 1940 onwards. However I have a photo of Ilex at Alexandria in her first ‘Alexandria’ scheme very clearly showing TSDS gear still in place:
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Ilex 1940 Alexandria TSDS winch - Copy.jpg [ 4.83 KiB | Viewed 5917 times ]
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Ilex 1940 Alexandria TSDS gear at stern davits folded down- Copy.jpg [ 6.39 KiB | Viewed 5917 times ]
Note the angle of the top of the stowed paravane and the mounting right at the stern with its overhanging brackets and their dangling snatch blocks through which the sweeping wires were fed.
In Brett’s 1941 photo I believe that at the stern you can see the distinctive angled silhouette formed by the top of a stowed paravane plus the mounting right at the stern and one of its aft projecting brackets.
The (lack of) visibility of the paravane davits is not a reliable guide as they could be folded down (Icarus overhead 19 Oct 1942):
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Icarus 1942 10 19 TSDS davits folded down a - Copy.jpg [ 188.74 KiB | Viewed 5917 times ]
Once folded down between the paravanes the davits become more-or-less invisible in low-angle views as this photo of Icarus 19 Oct 1942, taken by the same PR sortie as the overhead view, demonstrates:
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Icarus 1942 10 19 TSDS davits folded down b - Copy.jpg [ 10.99 KiB | Viewed 5917 times ]
Damaged in June 1941 Ilex slowly made her way to Charleston to be repaired. When she re-emerged in September 1942 she still had TSDS fitted. In this photo the paravane davits are upright.
https://www.iwm.org.uk/collections/item ... /205167531The written record supports this. Whilst the half-yearly CB 01815B (Particulars of War Vessels and Aircraft) may not be a useful guide to the exact dates of modifications or to local improvisations, as a record of the situation regarding major fittings/equipment at different points in time it normally gets there in the end. It records Ilex as fitted with TSDS throughout this period.