~てもかまいません (would it be okay)

The pattern ~てもかまわない / ~てもかまいません (also written ~ても構わない / ~ても構いません), literally 'even if X, [I/it] don't mind,' used either to ask permission ('would it be all right if?') or to give permission/reassurance ('it's fine if you X / it doesn't matter even if X'). 構わない literally means 'I don't mind.' Slightly more polite than ~てもいい/~てもいいですか.