Blood filters (10a, 10b) sized and configured to be positioned within a vascular vessel include a plurality of anchoring arms (22) having a removable sleeve (22-2) for temporarily anchoring the blood filter to a vessel wall. In especially preferred embodiments, the removable sleeve (22-2) is formed of bioabsorbable material. When the filter (10a, 10b) is deployed, it is this removable sleeve (22-2) which comes into contact with the inner tissue wall of the patient's blood vessel (typically the inferior vena cava). When it is desired to remove the filter, endothelization of the sleeve (22-2) has typically occurred but since the sleeves are a removable (separable) component part of the anchoring arms (22), the entire filter device (10a, 10b) can be retrieved thereby leaving the endothelized sleeves (22-2) remaining in place on the interior wall of the patient's vascular vesse. However, such sleeves (22-2) will be absorbed over time (preferably by means of hydrolysis) since they are formed of a bioabsorbable polymeric material. In such a manner, the filters (10a, 10b) of the present invention allow relatively easy retrieval while minimizing (if not preventing entirely) harm to the vascular endothelium.